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All Journal Matematika: Jurnal Teori dan Terapan AdMathEdu : Jurnal Ilmiah Pendidikan Matematika, Ilmu Matematika dan Matematika Terapan Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam Journal of the Indonesian Mathematical Society Jurnal KARISMATIKA Jurnal Sains Matematika dan Statistika Journal of Medives Jurnal Penelitian Pendidikan IPA (JPPIPA) Desimal: Jurnal Matematika MUST: Journal of Mathematics Education, Science and Technology Jurnal SOLMA BAREKENG: Jurnal Ilmu Matematika dan Terapan Jambura Journal of Mathematics JURNAL MATHEMATIC PAEDAGOGIC InPrime: Indonesian Journal Of Pure And Applied Mathematics Jurnal Pengabdian Masyarakat Multidisiplin Unri Conference Series: Community Engagement Journal of Science and Technology Mathematics and Applications (MAp) Journal Euclid Jurnal Matematika Integratif Journal of Medives: Journal of Mathematics Education IKIP Veteran Semarang Jcommits : The Journal of Community Empowerment, Innovation, and Sustainability
Sri Gemawati
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Derivasi di Pseudo BG-aljabar Putri, Ayuni; Gemawati, Sri; Syamsudhuha, Syamsudhuha
Jambura Journal of Mathematics Vol 7, No 1: February 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i1.28306

Abstract

A BG-algebra  is defined as a non-empty set  that includes a constant 0 and a binary operation  which adheres to the following axioms: (𝐵G1) , (𝐵G2) , and (𝐵G3)  for all . Pseudo BG-algebra is a generalization of BG-algebra, which is an algebra  that satisfies the following axioms: (pBG1) , (pBG2) , and (pBG3)  for all . In BG-algebra introduced an (l, r)-derivation, an (r, l)-derivation, and left derivation. This article aims to discuss and develop the concept of derivations in pseudo BG-algebras by introducing two new operations,  and , within the structure of pseudo BG-algebra . These operations are defined as  and  for each . In this research, the  operation in BG-algebra derivations replaced with the  and  operations under certain conditions, leading to the formulation of new types of derivations. Through this approach, three main types of derivations in pseudo BG-algebras are identified: (l, r)-derivation, (r, l)-derivation, and left derivation of type 1 and type 2. The results reveal several significant properties, including a formula for , the role of the special element 0, regularity in derivations, and the relationship between regular derivations and  as the identity function. This study contributes to advancing the theory of pseudo BG-algebras and its potential applications in other algebraic structures.
Konstruksi dan Analisis r-Ideal di BG-aljabar Beauty, Meivy Andhika; Gemawati, Sri; Deswita, Leli
Jambura Journal of Mathematics Vol 7, No 1: February 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i1.30097

Abstract

A non-empty set G with a binary operation ∗ and a constant 0 that satisfies the following axioms: , , and  for all  is called a BG-algebra. A non-empty subset I of G is said to be an ideal in G if it satisfies: (i)  and (ii)  and  implies  for all . This article introduces the new concept of r-ideal in BG-algebra, which is an extension of the ideal in BN-algebra. Unlike the definition of an ideal in BN-algebra, an r-ideal only requires a non-empty subset I of G without the need to satisfy the full ideal conditions. This study examines the properties of r-ideals and their relationships with subalgebras, normal, and ideals in BG-algebra. In the final part, it is concluded that every subalgebra is an r-ideal in BG-algebra, and every normal ideal is also an r-ideal.
Completely Closed Filter in BN -Algebra Ramadhan, Andi Rio; Gemawati, Sri; Kartini, Kartini
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 7, No 1 (2025)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v7i1.42170

Abstract

A BN-algebra (A; *,0) is a non-empty set A equipped with a binary operation * and a constant 0, which satisfies the following axioms: (B1)  a*a=0, (B2)  a*0=a, and (BN)  (a*b)*c=(0*c)*(b*a) for all a,b,c ∈A. A subset I of A is called an ideal in A if it satisfies (i) 0∈I, (ii) if b∈I and a*b∈I imply a∈I, for all a,b∈A. This paper presents an original investigation on the completely closed filter in BN-algebra, a topic that has not been extensively explored in previous research. The concepts of filter, closed filter, and completely closed filter in BN-algebra are defined, which can always be associated with the concept of an ideal in BN-algebra. It begins by defining a filter in BN-algebra and then providing additional conditions to make it a closed and completely closed filter. The results show that every filter in BN-algebra has a condition (D), and every non-empty subset of BN1-algebra is a closed filter. Furthermore, every normal ideal in BN-algebra, ideal in Coxeter algebra, and subalgebra in BN1-algebra is a completely closed filter.Keywords: BN-algebra; Completely closed filter; Filter; Ideal. AbstrakBN-Aljabar (A; *,0) adalah himpunan tak kosong A yang dilengkapi dengan operasi biner * dan konstanta 0, yang memenuhi aksioma berikut: (B1) a*a=0,(B2) a*0=a, dan (BN) (a*b)*c=(0*c)*(b*a) untuk setiap a,b,c ∈A. Subhimpunan I dari A disebut ideal di A jika memenuhi: (i) 0∈I, (ii) untuk setiap b∈I dan a*b∈I mengakibatkan a∈I, untuk setiap a,b∈A. Dalam artikel ini, kami menyajikan sebuah studi baru tentang filter tertutup lengkap dalam BN-aljabar, sebuah topik yang belum banyak dieksplorasi dalam penelitian sebelumnya. Konsep filter, filter tertutup, dan filter tertutup lengkap dalam BN-Aljabar didefinisikan, yang mana selalu dapat dikaitkan dengan konsep ideal dalam BN-Aljabar. Dimulai dengan mendefinisikan filter dalam BN-aljabar, kemudian memberikan kondisi tambahan untuk menjadikannya filter tertutup dan filter tertutup lengkap. Hasil yang diperoleh adalah setiap filter dalam BN-Aljabar dengan kondisi (D) dan setiap subset tak kosong dari BN1-aljabar merupakan filter tertutup. Lebih jauh, setiap ideal normal dalam BN-aljabar, ideal dalam Coxeter aljabar, dan subaljabar dalam BN1-aljabar merupakan filter tertutup lengkap.Kata Kunci: BN-aljabar; Filter tertutup lengkap; Filter; Ideal. 2020MSC: 03G25, 03G10
DERIVATIONS OF PSEUDO BE-ALGEBRAS Indryantika, Nessy; Gemawati, Sri; Kartini, Kartini
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1565-1574

Abstract

Pengembangan Bahan Ajar Matematika Bidang Kalkulus Tingkat SMA Melalui Pengabdian Masyarakat di Kabupaten Kepulauan Meranti Zulkarnain, Zulkarnain; Danil Hendry Gamal, Moh; M, Imran; Hasbiyati, Ihda; Gemawati, Sri; M, Musraini; Mu’tamar, Khozin
JCOMMITS: Journal of Community Empowerment, Inovation, and sustainability Vol. 3 No. 1 (2025): Jcommits (The Journal of Community Empowerment, Innovation, and Sustainability)
Publisher : LPPM UNIVERSITAS LANCANG KUNING

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Kalkulus merupakan salah satu materi penting dalam pembelajaran matematika di tingkat sekolah menengah atas, khususnya dalam pendidikan STEM. Namun, banyak guru mengalami kesulitan dalam menyusun soal yang dapat meningkatkan pemahaman konseptual siswa. Penelitian ini bertujuan untuk mengukur pemahaman guru terhadap konsep kalkulus serta kemampuan mereka dalam mengembangkan soal yang dimodifikasi melalui program pengabdian masyarakat. Studi ini melibatkan 23 guru matematika sekolah menengah atas di Kabupaten Kepulauan Meranti. Program ini terdiri dari tiga tahapan utama, yaitu: (1) asesmen awal menggunakan soal kalkulus yang mencakup persamaan, turunan, pertidaksamaan, dan kurva, (2) diskusi serta sesi pembelajaran terpandu, dan (3) latihan pembuatan soal modifikasi berdasarkan pertanyaan yang telah diberikan. Hasil penelitian menunjukkan bahwa beberapa guru memiliki pemahaman yang baik terhadap konsep dasar kalkulus, namun banyak yang mengalami kesulitan dalam memahami materi integral. Selain itu, kemampuan guru dalam menyusun soal modifikasi bervariasi. Temuan ini menegaskan pentingnya pelatihan profesional yang berkelanjutan serta kolaborasi antar lembaga pendidikan untuk meningkatkan keterampilan pedagogik guru dalam pengajaran kalkulus. Inisiatif lanjutan perlu difokuskan pada peningkatan kompetensi guru, terutama dalam memahami dan mengajarkan topik kalkulus yang lebih kompleks seperti aplikasi integral.
T-IDEAL AND α-IDEAL OF BP-ALGEBRAS Gemawati, Sri; M, Musraini; Putri, Ayunda; Marjulisa, Rike; Fitria, Elsi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss2pp1129-1134

Abstract

This paper explores the characteristics of two distinct ideal types within BP-algebra, specifically T-ideal and -ideal. Initially, we elucidate the characteristics of the T-ideal in BP-algebra, establishing its connections with the perfect, normal, and normal ideal in BP-algebra. Subsequently, we demonstrate that the kernel of a homomorphism in BP-algebra constitutes a T-ideal. Moving forward, we delineate the properties of -ideal in BP-algebra, highlighting its relationships with ideal and filter in the context of BP-algebra. Additionally, we explore the characteristics of -ideal and subalgebra in 0-commutative BP-algebra. Finally, it is proven that the kernel of a homomorphism in 0-commutative BP-algebra can be identified as an -ideal.
Completely Closed Filter in BN -Algebra Ramadhan, Andi Rio; Gemawati, Sri; Kartini, Kartini
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol. 7 No. 1 (2025)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v7i1.42170

Abstract

A BN-algebra (A; *,0) is a non-empty set A equipped with a binary operation * and a constant 0, which satisfies the following axioms: (B1) a*a=0, (B2) a*0=a, and (BN) (a*b)*c=(0*c)*(b*a) for all a,b,c ∈A. A subset I of A is called an ideal in A if it satisfies (i) 0∈I, (ii) if b∈I and a*b∈I imply a∈I, for all a, b ∈ A. This paper presents an original investigation on the completely closed filter in BN-algebra, a topic that has not been extensively explored in previous research. The concepts of filter, closed filter, and completely closed filter in BN-algebra are defined, which can always be associated with the concept of an ideal in BN-algebra. It begins by defining a filter in BN-algebra and then providing additional conditions to make it a closed and completely closed filter. The results show that every filter in BN-algebra has a condition (D), and every non-empty subset of BN1-algebra is a closed filter. Furthermore, every normal ideal in BN-algebra, ideal in Coxeter algebra, and subalgebra in BN1-algebra is a completely closed filter.Keywords: BN-algebra; completely closed filter; filter; ideal.AbstrakBN-Aljabar (A; *,0) adalah himpunan tak kosong A yang dilengkapi dengan operasi biner * dan konstanta 0, yang memenuhi aksioma berikut: (B1) a*a=0,(B2) a*0=a, dan (BN) (a*b)*c=(0*c)*(b*a) untuk setiap a,b,c ∈A. Subhimpunan I dari A disebut ideal di A jika memenuhi: (i) 0∈I, (ii) untuk setiap b∈I dan a*b∈I mengakibatkan a∈I, untuk setiap a,b∈A. Dalam artikel ini, kami menyajikan sebuah studi baru tentang filter tertutup lengkap dalam BN-aljabar, sebuah topik yang belum banyak dieksplorasi dalam penelitian sebelumnya. Konsep filter, filter tertutup, dan filter tertutup lengkap dalam BN-Aljabar didefinisikan, yang mana selalu dapat dikaitkan dengan konsep ideal dalam BN-Aljabar. Dimulai dengan mendefinisikan filter dalam BN-aljabar, kemudian memberikan kondisi tambahan untuk menjadikannya filter tertutup dan filter tertutup lengkap. Hasil yang diperoleh adalah setiap filter dalam BN-Aljabar dengan kondisi (D) dan setiap subset tak kosong dari BN1-aljabar merupakan filter tertutup. Lebih jauh, setiap ideal normal dalam BN-aljabar, ideal dalam Coxeter aljabar, dan subaljabar dalam BN1-aljabar merupakan filter tertutup lengkap.Kata Kunci: BN-aljabar; filter tertutup lengkap; filter; ideal.2020MSC: 03G25, 03G10
The k-Tribonacci Matrix and the Pascal Matrix Gemawati, Sri; Musraini, Musraini; Mirfaturiqa, Mirfaturiqa
Jambura Journal of Mathematics Vol 6, No 1: February 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v6i1.24131

Abstract

This article discusses the relationship between the k-Tribonacci matrix Tn(k) and the Pascal matrix Pn, by first constructing the k-Tribonacci matrix and then looking for its inverse. From the inverse k-Tribonacci matrix, unique characteristics can be constructed so that general shapes can be constructed, and then from the relationship of the k-Tribonacci matrix Tn(k) and the Pascal matrix Pn obtain a new matrix, i.e. Un(k). Furthermore, a factor is derived from the relationship of the k-Tribonacci matrix Tn(k) and the Pascal matrix Pn i.e. Pn = Tn(k)Un(k).
The Existence of Cocyclic Formed by Angle Trisectors in a Butterfly Quadrilateral and its Application in Physics Mardani Fitra; Mashadi; Sri Gemawati
Jurnal Penelitian Pendidikan IPA Vol 11 No 2 (2025): February
Publisher : Postgraduate, University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/jppipa.v11i2.9909

Abstract

One of the most intriguing results related to angle trisectors in convex quadrilaterals is Morley's Theorem, which several authors have subsequently extended to non-convex quadrilaterals. Numerous studies have explored the side lengths of angle bisectors, angle trisectors, and the area ratios formed by angle trisectors in both convex and non-convex quadrilaterals. However, no research has discussed the problem of angle trisectors in butterfly quadrilaterals. Therefore, this paper aims to extend the concept of angle trisectors to butterfly quadrilaterals. Various other quadrilaterals will be formed from the construction of these angle trisectors. By employing the concept of concyclic, we will demonstrate the existence of several concyclic quadrilaterals arising from this trisector construction. Triangle angles in butterfly quadrilaterals in geometry play an important role in physics. Geometry provides a visual and mathematical language that allows us to describe, analyze, and understand various physical phenomena.
SUATU KAJIAN DERIVASI YANG DIINDUKSI OLEH ENDOMORFISMA PADA PSEUDO BG-ALJABAR Ramadhani Fitri Fitri; Sri Gemawati; Susilawati Susilawati
MUST: Journal of Mathematics Education, Science and Technology Vol 10 No 2 (2025): DECEMBER
Publisher : Universitas Muhammadiyah Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30651/must.v10i2.30742

Abstract

Penelitian ini mengembangkan konsep derivasi pada pseudo BG-aljabar melalui pendekatan berbasis endomorfisma. BG-aljabar (P; ∗, 0) adalah himpunan tak kosong P dengan operasi biner ∗ dan konstanta 0 yang memenuhi aksioma (BG1) p ∗ p = 0, (BG2) p ∗ 0 = p, dan (BG3) (p ∗ q) ∗ (0 ∗ q) = p untuk setiap p, q ∈ P. Pseudo BG-aljabar (R; ∗, ⋄, 0) merupakan generalisasi BG-aljabar dengan dua operasi biner yang memenuhi (PBG1) p ∗ 0 = p ⋄ 0 = p, (PBG2) p ∗ p = p ⋄ p = 0, dan (PBG3) (p ∗ q) ⋄ (0 ∗ q) = (p ⋄ q) ∗ (0 ⋄ q) = p untuk setiap p, q ∈ R. Penelitian ini memperkenalkan dua jenis derivasi utama, yaitu f-derivasi dan (f, g)-derivasi, yang masing-masing dikonstruksi melalui operasi gabungan (⊛) dan operasi simetris (⊙). Metode penelitian menggunakan pendekatan aksiomatik-deduktif dengan teknik pembuktian teorema berbasis sistem aksioma pseudo BG-aljabar. Hasil penelitian menunjukkan bahwa pendekatan menggunakan endomorfisma, baik dengan satu fungsi f maupun pasangan fungsi (f, g), menghasilkan kerangka derivasi yang konsisten dan dapat dikarakterisasi secara sistematis. Teorema fundamental membuktikan bahwa f-derivasi kiri reguler identik dengan endomorfisma penginduksinya. Kerangka teoretis yang dihasilkan memberikan landasan untuk eksplorasi derivasi pada struktur aljabar pseudo lainnya.
Co-Authors Abd. Ghafur Bin Ahmad Abd. Ghafur Bin Ahmad Abdul Hadi Ade Nova Rahma Ade Novia Rahma Agusni ' Alberta Rika Pratiwi Ali Subroto Amalina Amalina, Amalina Amirah Diniaty Andriani, Dessy Ani Ani Ardiansyah Yan Hakim Nasution Asli Sirait Ayunda Putri Ayunda Putri Barutu, Fabelia Andani Beauty, Meivy Andhika Bona Martua Siburian Chitra Valentika Danil Hendry Gamal, Moh Delisa Pratiwi Dessy Andriani Dessy Andriani . Egytia Yattaqi Elsi Fitria Endah Dwi Jayanti Endang Lily Fabelia Andani Barutu Gamal, M.D.H Hasriati Hasriati Hendra Maryulis Husnul Khatimah Husnul Khatimah Ihda Hasbiyati Indryantika, Nessy Irma . Fitri IRSAN TAUFIK ALI Jufri Jufri Jufri Jufri Jufri, Jufri Kartini Kartini Kartini Leli Deswita Lydia . Ariftalia M. D. H. . Gamal M. Imran M. Mashadi M.D.H Gamal M.D.H Gamal Mahiroh Mardani Fitra Mas hadi Mashadi Mashadi ' Mashadi Mashadi Mashadi Mashadi Mashadi Mashadi Mashadi Mashadi Mashadi Mashadi Mashadi Mashadi Mashadi Mashadi Mirfaturiqa Mirfaturiqa, Mirfaturiqa Misra Herlina Musraini M Musraini, M Musraini, Musraini Mu’tamar, Khozin novelia . . Novita Yuliardani Novrialman ' Nur Meliana Sari Nurbai, Reihani Jemila Oki Rasdana Pratiwi, Delisa Puteri Januarti Putri, Ayuni Rahmayani, Indah Rahmi Rahmi Ramadhan, Andi Rio Ramadhani Fitri Fitri Rika Pratiwi Rika Pratiwi Rike Marjulisa Rita Desfitri Riza . Gushelsi Rora Oktafia Selva Amelia Sandi Silfia Rini Sri . Handayani Sri Mawarni Sri Sukmawati Sugianti, Khoirunnisa Surlina Surlina Susanto, Andi Susilawati, S. Syamsudhuha Syamsudhuha Syamsudhuha Welly Desriyati Wellya Aziz weriono weriono Wita . Maywidia Yeni . Azrida Yuliardani, Novita Yulismansyah ' Yuslenita Muda Zubaidah Amir Zulkarnain Zulkarnain