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<![CDATA[PEMBELAJARAN STRUKTUR ALJABAR DENGAN MENGGUNAKAN SOFTWARE GAP ]]>
<![CDATA[Carnia, Ema]]>;
<![CDATA[Aisah, Isah]]>;
<![CDATA[Sylviani, Sisilia]]>
<![CDATA[ Jurnal Pengajaran Matematika dan Ilmu Pengetahuan Alam Vol 19, No 2 (2014): Jurnal Pengajaran MIPA ]]>
Publisher : <![CDATA[Faculty of Mathematics and Science Education, Universitas Pendidikan Indonesia ]]>
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DOI: 10.18269/jpmipa.v19i2.455
<![CDATA[Strukur Aljabar sebagai salah satu mata kuliah wajib yang diberikan di Program Studi Matematika di Indonesia dirasakan sulit oleh sebagian besar mahasiswa. Sebagai salah satu alternatif untuk mengatasi hal itu maka diperkenalkan penggunaan software GAP (Group, Algorithm, and Programming) dalam proses belajar mengajar pada mata kuliah Strukur Aljabar. Selain mendukung dalam proses pembelajaran, penggunaan software GAP ini mendukung pemberlakuan Kurikulum Berbasis Kompetensi (KBK) di Perguruan Tinggi, khususnya di Program Studi Matematika, yang secara tidak langsung menuntut pembelajaran Student Centered Learning (SCL). Pengajaran dengan menggunakan software ini akan diujicobakan di Departemen Matematika FMIPA UNPAD. Dengan demikian diharapkan dapat memberikan motivasi untuk belajar Struktur Aljabar dengan cara yang tidak membosankan yang pada akhirnya dapat meningkatkan pemahaman mahasiswa terhadap mata kuliah tersebut. Penelitian ini baru sebatas kajian teori dan belum diimplementasikanKata kunci: GAP, Struktur Aljabar.]]>
<![CDATA[Kongruensi Unsur Idempoten Ortogonal dalam Aljabar Insidensi Finitary ]]>
<![CDATA[Carnia, Ema]]>;
<![CDATA[Wahyuni, Sri]]>;
<![CDATA[Irawati, Irawati]]>;
<![CDATA[Setiadji, Setiadji]]>
<![CDATA[ Jurnal Natur Indonesia Vol 13, No 2 (2011) ]]>
Publisher : <![CDATA[Lembaga Penelitian dan Pengabdian kepada Masyarakat Universitas Riau ]]>
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DOI: 10.31258/jnat.13.2.89-93
<![CDATA[Let X be a partially ordered set, R is a commutative ring with identity and FININC (X, R) denote finitary incidencealgebra of poset X over R. In this paper it will be seen congruence of two elements that are idempotent orthogonalin FININC (X, R) relative to the modulo Radical Jacobson of algebra. Review of this topic would be useful to examineisomorphism problems of the finitary incidence Algebra.]]>
<![CDATA[PEMBELAJARAN STRUKTUR ALJABAR DENGAN MENGGUNAKAN SOFTWARE GAP ]]>
<![CDATA[Carnia, Ema]]>;
<![CDATA[Aisah, Isah]]>;
<![CDATA[Sylviani, Sisilia]]>
<![CDATA[ Jurnal Pengajaran MIPA Vol 19, No 2 (2014): JPMIPA: Volume 19, Issue 2, 2014 ]]>
Publisher : <![CDATA[Faculty of Mathematics and Science Education, Universitas Pendidikan Indonesia ]]>
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DOI: 10.18269/jpmipa.v19i2.36174
<![CDATA[ABSTRAKStrukur Aljabar sebagai salah satu mata kuliah wajib yang diberikan di Program Studi Matematika di Indonesia dirasakan sulit oleh sebagian besar mahasiswa. Sebagai salah satu alternatif untuk mengatasi hal itu maka diperkenalkan penggunaan software GAP (Group, Algorithm, and Programming) dalam proses belajar mengajar pada mata kuliah Strukur Aljabar. Selain mendukung dalam proses pembelaja-ran, penggunaan software GAP ini mendukung pemberlakuan Kurikulum Berbasis Kompetensi (KBK) di Perguruan Tinggi, khususnya di Program Studi Matematika, yang secara tidak langsung menuntut pembelajaran Student Centered Learning (SCL). Pengajaran dengan menggunakan software ini akan diujicobakan di Departemen Matematika FMIPA UNPAD. Dengan demikian diharapkan dapat mem-berikan motivasi untuk belajar Struktur Aljabar dengan cara yang tidak membosankan yang pada akhirnya dapat meningkatkan pemahaman mahasiswa terhadap mata kuliah tersebut. Penelitian ini baru sebatas kajian teori dan belum diimplementasikanABSTRACTAs one of the compulsory subjects given in the Mathematical Studies Program in Indonesia, Algebraic Structure is perceived as difficult by most students. One alternative to overcome it is by introducing the use of GAP software (Group, Algorithm, and Programming) in teaching and learning for Algebraic Structure course. In addition to support the learning process, the use of GAP software support the implementation of the Competency Based Curriculum in universities, especially in Mathematics Program, which indirectly requires Student Centered Learning (SCL). Teaching with this software will be tested in Department of Mathematics Faculty of Mathematical and Natural Sciences. Hence the use of it is expected to provide the motivation to learn algebraic structure in a way that is not boring, and will subsequently increase students’ understanding of the course. This research is a theoretical study and has not been implemented yet.]]>
<![CDATA[Karakterisasi Subgrup Sylow Solvable Dari Grup Poin Senyawa Fosfor Pentaklorida ]]>
<![CDATA[Ema Carnia Carnia]]>;
<![CDATA[Sisilia Sylviani]]>;
<![CDATA[Elah Dewia]]>
<![CDATA[ Jurnal Sains Dasar Vol 6, No 2 (2017): October 2017 ]]>
Publisher : <![CDATA[Faculty of Mathematics and Natural Science, Universitas Negeri Yogyakarta ]]>
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DOI: 10.21831/jsd.v6i2.15295
<![CDATA[Setiap molekul atau senyawa kimia memiliki operasi simetri yang mendeskripsikan keseluruhan karakter dari molekul tersebut. Himpunan dari semua operasi simetri yang berlaku pada suatu senyawa akan membentuk suatu grup. Semua operasi simetri yang berlaku pada senyawa Fosfor pentaklorida membentuk grup poin. Pada paper ini dibahas karakterisasi dari grup poin senyawa Fosfor pentaklorida dilihat dari sudut pandang teori grup. Salah satu hasil yang diperoleh adalah bahwa setiap subgrup Sylow dari senyawa Fosfor pentaklorida merupakan grup solvable.Kata kunci: simetri, grup poin, teori grup, p-subgrup Sylow, solvableCHARACTERIZATION OF SOLVABLE SYLOW SUBGROUP OF POINT GROUP PHOSPHORUS PENTACHLORIDE COMPOUNDPhosphorus pentachloride is a gaseous chemical compound. One of the uses of this compound is a substance that can accelerate the rate of chemical reactions. Phosphorus pentachloride compounds has a molecular geometry shape trigonal bipyramid with a total of 12 symmetry operations. The set of all symmetry operations completed with the operation of the function composition will form a group called the D_3h point group. In this paper discuss the characterization the points group of Phosphorus pentachloride compound from the perspective of group theory. Beginning with point group proofing, then determine all Sylow p-subgroup and normal subgroups of this group.The results obtained were the properties that Sylow 2-subgroup and Sylow 3-subgroup of Phosphorus pentachloride compounds and slices between Sylow subgroups and normal subgroup is solvable groups. Keywords: Phosphorus pentachloride, point group, group theory, Sylow p-subgroup, solvable]]>
<![CDATA[PENGGUNAAN GROUP, ALGORITHM, AND PROGRAMMING (GAP) DALAM PEMBELAJARAN GRUP KUOSIEN ]]>
<![CDATA[Sisilia . Sylviani]]>;
<![CDATA[Ema . Carnia]]>;
<![CDATA[Isah . Aisah]]>
<![CDATA[ KARISMATIKA: Kumpulan Artikel Ilmiah, Informatika, Statistik, Matematika dan Aplikasi Vol 1, No 2 (2015): Karismatika ]]>
Publisher : <![CDATA[Universitas Negeri Medan ]]>
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DOI: 10.24114/jmk.v1i2.17067
<![CDATA[ABSTRAK Pada paper ini akan dibahas suatu alternative metode pembelajaran yang dapat digunakan dalam menyampaikan materi Grup Kuosien/ Grup Faktor pada matakuliah Struktur Aljabar. Grup Kuosien sebagai salah satu materi dalam Struktur Aljabar sering kali dirasakan sulit oleh sebagian besar mahasiswa S1 Jurusan Matematika. Untuk itu, diperlukan suatu metoda pembelajaran yang dapat memudahkan mahasiswa untuk memahami materi tersebut. Salah satu alternatif yang dapat dilakukan adalah dengan menggunakan software GAP (Group, Algorithm, and Programming) sebagai alat bantú dalam mempelajar imateri Grup Kuosien. GAP dapat membuat penyajian konsep grup kuosien menjadi lebih menarik. Sehingga, diharapkan dapat lebih memudahkan mahasiswa untuk memahami konsep Grup Kuosien.Keywords: Grup Kuosien, Group algorithm and programming, Struktur Aljabar ABSTRACT This paper will discuss an alternative method of learning which can be used in presenting the Quotient Group/ Factor Group material in Abstract Algebra course. Quotient group as one of the materials in Abstract Algebra is often perceived difficult by most of undergraduate mathematics students. For that, we need a method of learning which can facilitate the students to understand the material. One of the alternatives that can be done is by using GAP (Group, Algorithm, and programming) software as a tool in studying the quotient group material. GAP can make a presentation of the quotient group concept becomes more attractive. Thus, it can be easier for students to understand the concept of quotient group.Keywords: Quotient Group, Group Algorithm And Programming, Abstract Algebra]]>
<![CDATA[The Existence of Affine Structures on the Borel Subalgebra of Dimension 6 ]]>
<![CDATA[Edi Kurniadi]]>;
<![CDATA[Ema Carnia]]>;
<![CDATA[Herlina Napitupulu]]>
<![CDATA[ ComTech: Computer, Mathematics and Engineering Applications Vol. 12 No. 1 (2021): ComTech ]]>
Publisher : <![CDATA[Bina Nusantara University ]]>
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DOI: 10.21512/comtech.v12i1.6581
<![CDATA[The notion of affine structures arises in many fields of mathematics, including convex homogeneous cones, vertex algebras, and affine manifolds. On the other hand, it is well known that Frobenius Lie algebras correspond to the research of homogeneous domains. Moreover, there are 16 isomorphism classes of 6-dimensional Frobenius Lie algebras over an algebraically closed field. The research studied the affine structures for the 6-dimensional Borel subalgebra of a simple Lie algebra. The Borel subalgebra was isomorphic to the first class of Csikós and Verhóczki’s classification of the Frobenius Lie algebras of dimension 6 over an algebraically closed field. The main purpose was to prove that the Borel subalgebra of dimension 6 was equipped with incomplete affine structures. To achieve the purpose, the axiomatic method was considered by studying some important notions corresponding to affine structures and their completeness, Borel subalgebras, and Frobenius Lie algebras. A chosen Frobenius functional of the Borel subalgebra helped to determine the affine structure formulas well. The result shows that the Borel subalgebra of dimension 6 has affine structures which are not complete. Furthermore, the research also gives explicit formulas of affine structures. For future research, another isomorphism class of 6-dimensional Frobenius Lie algebra still needs to be investigated whether it has complete affine structures or not.]]>
<![CDATA[Levi Decomposition of Frobenius Lie Algebra of Dimension 6 ]]>
<![CDATA[Henti Henti]]>;
<![CDATA[Edi Kurniadi]]>;
<![CDATA[Ema Carnia]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 3 (2022): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v7i3.15656
<![CDATA[In this paper, we study notion of the Lie algebra of dimension 6. The finite dimensional Lie algebra can be expressed in terms of decomposition between Levi subalgebra and the maximal solvable ideal. This form of decomposition is called Levi decomposition. The work aims to obtain Levi decomposition of Frobenius Lie algebra of dimension 6. To achieve this aim, we compute Levi subalgebra and the maximal solvable ideal (radical) of with respect to its basis. To obtain Levi subalgebra and the maximal solvable ideal, we apply literature reviews about Lie algebra and decomposition Levi in Dagli result. For future research, decomposition Levi for higher dimension of Frobenius Lie algebra is still an open problem.]]>
<![CDATA[Mathematical Model of Iteroparous and Semelparous Species Interaction ]]>
<![CDATA[Arjun Hasibuan]]>;
<![CDATA[Asep Kuswandi Supriatna]]>;
<![CDATA[Ema Carnia]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 3 (2022): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v7i3.16447
<![CDATA[A species can be categorized based on its reproductive strategy, including semelparous and iteroparous. Semelparous species is a species that reproduces only once in its lifetime shortly before dying, while iteroparous species is a species that reproduces in its lifetime more than once. In this paper, we examine multispecies growth dynamics involving both species categories focusing on one semelparous species and one iteroparous species influenced by density-dependent also harvesting in which there are two age classes each. We divided the study into two models comprising competitive and non-competitive models of both species. Competition in both species can consist of competition within the same species (intraspecific competition) and competition between different species (interspecific competition). Our results show that the level of competition both intraspecific and interspecific affects the co-existence equilibrium point and the local stability of the co-existence equilibrium point.]]>
<![CDATA[Characteristic of Quaternion Algebra Over Fields ]]>
<![CDATA[Muhammad Faldiyan]]>;
<![CDATA[Ema Carnia]]>;
<![CDATA[Asep K. Supriatna]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 4 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v7i4.17625
<![CDATA[Quaternion is an extension of the complex number system. Quaternion are discovered by formulating 4 points in 4-dimensional vector space using the cross product between two standard vectors. Quaternion algebra over a field is a 4-dimensional vector space with bases and the elements of the algebra are members of the field. Each element in quaternion algebra has an inverse, despite the fact that the ring is not commutative. Based on this, the purpose of this study is to obtain the characteristics of split quaternion algebra and determine how it interacts with central simple algebra. The research method used in this paper is literature study on quaternion algebra, field and central simple algebra. The results of this study establish the equivalence of split quaternion algebra as well as the theorem relating central simple algebra and quaternion algebra. The conclusion obtained from this study is that split quaternion algebra has five different characteristics and quaternion algebra is a central simple algebra with dimensions less than equal to four.]]>
<![CDATA[Keterkaitan Grup Spesial Uniter dengan Grup Spesial Ortogonal ]]>
<![CDATA[Nuraesa Nufus Faurani]]>;
<![CDATA[Ema Carnia]]>;
<![CDATA[Agus Supriatna]]>
<![CDATA[ Jurnal Matematika Integratif Vol 12, No 2: Oktober, 2016 ]]>
Publisher : <![CDATA[Department of Matematics, Universitas Padjadjaran ]]>
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DOI: 10.24198/jmi.v12.n2.11928.117-124
<![CDATA[Grup Lie merupakan grup yang berisikan matriks yang merepresentasikan pergerakan atauperputaran suatu titik terhadap sumbu koordinat atau sumbu koordinat terhadap suatu titik. Grup spesialuniter dan grup spesial ortogonal merupakan contoh grup Lie. Dalam kajian fisika, grup spesial uniter dimensidua (��(2)) merepresentasikan rotasi elektron terhadap pusat rotasinya. Sedangkan grup spesial ortogonaldimensi tiga (��(3)) merepresentasikan rotasi elektron terhadap inti atom. Dalam paper ini, akan dikajiketerkaitan antara kedua grup ini dengan menggunakan Teorema Isomorfisma sehingga diperolah hasil bahwaterdapat homomorfisma surjektif dari grup ��(2) ke grup ��(3) kemudian dapat ditunjukkan bahwa��(2)���(�) isomorfik dengan SO(3).]]>
