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All Journal Pythagoras: Jurnal Matematika dan Pendidikan Matematika MATEMATIKA Journal of the Indonesian Mathematical Society Journal of Natural Sciences and Mathematics Research Al-Jabar : Jurnal Pendidikan Matematika BAREKENG: Jurnal Ilmu Matematika dan Terapan Jurnal Pengabdian Masyarakat MIPA dan Pendidikan MIPA JTAM (Jurnal Teori dan Aplikasi Matematika) Jambura Journal of Mathematics Jurnal Pengabdian Kepada Masyarakat (JPKM) Tabikpun Pattimura Proceeding : Conference of Science and Technology Jurnal Sosial dan Sains Jurnal Pengabdian West Science Integra: Journal of Integrated Mathematics and Computer Science Limits: Journal of Mathematics and Its Applications
Nikken Prima Puspita
Departemen Matematika, Fakultas Sains Dan Matematika, Universitas Diponegoro, Indonesia
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QUOTIENT SEMINEAR-RINGS OF THE ENDOMORPHISM OF SEMINEAR-RINGS Fatimah, Meryta Febrilian; Hasnani, Fitriana; Puspita, Nikken Prima
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 16 No 3 (2022): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (446.98 KB) | DOI: 10.30598/barekengvol16iss3pp887-896

Abstract

A seminear-ring is a generalization of ring. In ring theory, if is a ring with the multiplicative identity, then the endomorphism module is isomorphic to . Let be a seminear-ring. Here, we can construct the set of endomorphism from to itself denoted by . We show that if is a seminear-ring, then is also a seminear-ring over addition and composition function. We will apply the congruence relation to get the quotient seminear-ring endomorphism. Furthermore, we show the relation between c-ideal and congruence relations. So, we can construct the quotient seminear-ring endomorphism with a c-ideal.
DERIVATION ON SEVERAL RINGS Thomas, Abdiel Bellamy; Puspita, Nikken Prima; Fitriani, Fitriani
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 3 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss3pp1729-1738

Abstract

Research on ring derivation is one of the studies that is quite popular among algebra lovers. The definition of the derivation on the ring is motivated by the derivation in calculus which has Leibniz's rule. The purpose of this paper is to show some of the derivation properties on several rings, namely divisor rings, cartesian product rings, and factor rings. Let be a commutative ring with multiplicative identity and A the set of multiplicative closed that has non-zero divisor. In this paper, we have shown some results of derivation on ring theory. If is a ring derivation of R and is a divisor ring of , we can construct for all , then the map is a derivation on . The concept of embedding one ring into another ring can be used so that the ring of constant of , namely , is a subring of the divisor ring . Related to the ideal on ring theory, if I is an ideal of R, then where is also a derivation on the ring . The last result in this paper comes from the ring of cartesian product, take be a ring with derivation for . The cartesian product ring have a derivation ring defined by for any .
THE CLEANNESS OF THE SUBRINGS OF M_2 (Z_P) Alfiana, Shinta Nur; Puspita, Nikken Prima; Widowati, Widowati
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/barekengvol18iss2pp1307-1316

Abstract

Let be a ring. Ring is said to be a clean ring if every element of R can be expressed as the sum of a unit and an idempotent element. Furthermore, there are r-clean rings. An r-clean ring is a generalization of a clean ring. In an r-clean ring, all of its elements can be represented as the sum of a regular element and an idempotent element. Moreover, strongly r-clean rings were introduced. A strongly r-clean ring is a ring where every element of the ring can be expressed as the sum of a regular and an idempotent element, and the multiplication of that regular and idempotent is commutative. On the other hand, there is a ring of the set of matrices over ring denotes by . In this paper, we will discuss the cleanness properties, especially strongly r-clean of the subring of . The aims of this paper are to find the characteristics of strongly r-clean of the subring of . Here, we assumed that is a ring of matrix over .
Constructing DNA Codes with Larger Distance from Quaternary Words Pradipta, Benediktus Panji; Puspita, Nikken Prima
Jambura Journal of Mathematics Vol 7, No 2: August 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i2.33132

Abstract

In this work, we propose a novel method to construct DNA codes from quaternary words. The method uses permutation groups that act in the set {1, 2, …, 4n}, representing the coordinate and coordinate value of quaternary words. The DNA code is obtained by finding a clique of the construction graph and mapping it using the bijective map 0 → A, 1 → C, 2 → T, 3 → G. We present a new approach to construct DNA codes with larger Hamming distance and reverse-complement distance compared to previously obtained DNA codes. This is achieved by using a modified construction graph tailored to the desired distance parameter. As a result, we can refine a DNA code to have improved Hamming distance and reverse-complement distance while maintaining the fixed GC-content constraint. This method simplifies the search for DNA codes with large distance parameters.
Key Matrix Generation Using Random Functions in Hill Cipher Modulo 95 Cryptography Bahtiar, Nurdin; Widodo, Aris Puji; Puspita, Nikken Prima
Integra: Journal of Integrated Mathematics and Computer Science Vol. 2 No. 1 (2025): March
Publisher : Magister Program of Mathematics, Universitas Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/integrajimcs.20252111

Abstract

In symmetric cryptography, the confidentiality of the chosen key and the security of its delivery mechanism are paramount to minimize the risk of unauthorized disclosure. Typically, in such systems, the sender and recipient focus primarily on the message (plaintext and ciphertext) rather than the complexities associated with key management. This approach aims to alleviate the burden of selecting a suitable and robust key for communicating parties. This study introduces a Hill Cipher modulo 95 cryptography method employing a matrix-based key, where key generation is achieved through a quantifiable randomization algorithm. The developed 2x2 key matrix facilitates a substantial number of possible keys, specifically 954 (exceeding 81 million). The key matrix generation process incorporates several functions, including those for ASCII character conversion, prime number verification, relative primality checks, modulo arithmetic, inverse modulo computation, determinant calculation, and inverse matrix determination. To simulate the encryption and decryption process, a desktop application was developed using the Lazarus Development IDE version 3.6. The application demonstrates effective generation of the required key matrix.
The Cleanness Property of The Integers Modulo n (ℤn) 'Aliyah, Dheva Ufiz; Puspita, Nikken Prima; Tjahjana, Redemtus Heru
Integra: Journal of Integrated Mathematics and Computer Science Vol. 1 No. 2 (2024): July
Publisher : Magister Program of Mathematics, Universitas Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/integrajimcs.20241214

Abstract

Assume that R is a ring with identity. A ring R is said to be clean when each of its elements can be written as the sum of an idempotent and a unit element within the ring. A stronger condition, known as strongly clean, requires that these elements commute under multiplication. As a special case, a module M over ring R is called a clean module when the endomorphism ring of the M is a clean module over R. Moreover, when the ring endomorphism of R-module M is a strongly clean, then the module M is referred to as a strongly clean. We know that the integers modulo n, denoted by ℤn, is a ring by the set of congruence classes modulo n, with standard addition and multiplication operations. In this study, we explore the cleanness properties of the ring ℤn and establish that it is a strongly clean ring. Furthermore, we study about the cleanness of ℤn as a module over ℤ and investigate the strongly cleanness of it module.
Pembelajaran Koordinat Kartesius dengan Menggunakan Pixel Art untuk Siswa Sekolah Dasar 'Aliyah, Dheva Ufiz; Alfiana, Shinta Nur; Alhusna, Lathifatul Inayah; Paramita, Arum Qurrotulaini Pradjna; Utami, Ratna Zakiyya Meilia; Puspita, Nikken Prima; Ratnasari, Lucia
Jurnal Pengabdian Kepada Masyarakat (JPKM) TABIKPUN Vol. 6 No. 1 (2025)
Publisher : Faculty of Mathematics and Natural Sciences - Universitas Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.23960/jpkmt.v6i1.216

Abstract

Pembelajaran koordinat kartesius merupakan salah satu materi dasar dalam matematika yang diajarkan di sekolah dasar. Pembelajaran koordinat kartesius dapat dilakukan dengan banyak cara. Pengabdian yang kami lakukan, memberikan alternatif pembelajaran mengenai koordinat kartesius. Alternatif pembelajaran tersebut menggabungkan pembelajaran koordinat kartesius dengan pixel art. Kegiatan pengabdian masyarakat ini menyasar pada siswa-siswi Kelas 5 SD Muhammadiyah 16 Karangasem, Kota Surakarta. Tujuan dari kegiatan ini yaitu untuk meningkatkan pemahaman dan motivasi siswa dalam pembelajaran koordinat kartesius melalui pendekatan kreatif dengan Pixel Art dan Mystery Cartesian Coordinate Games. Selain itu, siswa juga dapat mengetahui penerapan matematika melalui pixel art. Hasil kegiatan menunjukkan peningkatan minat belajar, kerja sama, dan pemahaman konsep koordinat kartesius, serta menjadikan pembelajaran matematika lebih interaktif dan menyenangkan.
Eksistensi Invers Moore Penrose Diperumum Elemen Normal Diperumum pada Ring dengan Involusi Titi Udjiani SRRM; Nikken Prima Puspita; Suryoto
Limits: Journal of Mathematics and Its Applications Vol. 20 No. 1 (2023): Limits: Journal of Mathematics and Its Applications Volume 20 Nomor 1 Edisi Ma
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

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

Abstract

The Moore Penrose inverse of normal element in ring with involution have been discussed by several researchers. By generalizing concept of Moore Penrose inverse to the generalized Moore Penrose inverse, the element properties of the generalized Moore Penrose inverse of normal elements have also been obtained. In addition to generalizing the concept of Moore Penrose inverse, the definition of the normal element has also been generalized by generalizing the power of 1 to n e N. It is found that intersection between set of generalized normal element and set of generalized Moore Penrose inverse element is not empty. This indicates that both of them have common properties, so this paper aims is to build the necessary and sufficient conditions for a generalized normal element to have a generalized Moore Penrose inverse using these properties. The method used is to look for the similarity of properties possessed by a generalized normal element and element that has generalized Moore Penrose inverse. The next step is to use the involution properties to obtain the final result. The approach taken is not only through the generalized Moore Penrose inverse, but also group inverse.
The Ideal Over Semiring of the Non-Negative Integer Adillah, Aisyah Nur; Hasnani, Fitriana; Fatimah, Meryta Febrilian; Puspita, Nikken Prima
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 3 (2023): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i3.14997

Abstract

Assumed that (S,+,.) is a semiring. Semiring is a algebra structure as a generalization of a ring. A set I⊆S is called an ideal over semiring S if for any α,β∈I, we have α-β∈I and sα=αs∈I for every s in semiring S.  Based on this definition, there is a special condition namely prime ideal P, when for any αβ∈P, then we could prove that α or β are elements of ideal P. Furthermore, an ideal I of S is irreducible if Ia is an intersection ideal from any ideal A and B on S, then I=A or I=B. We also know the strongly notion of the irreducible concept. The ideal I of S is a strongly irreducible ideal when I is a subset of the intersection of A and B (ideal of S), then I is a subset of A, or I is a subset of B. In this paper, we discussed the characteristics of the semiring of the non-negative integer set. We showed that pZ^+ is an ideal of semiring of the non-negative integer Z^+ over addition and multiplication. We find a characteristic that 〖pZ〗^+  is a prime ideal and also a strongly irreducible ideal of the semiring Z^+ with p is a prime number.
Singh's Fuzzy Time Series Forecasting Modification Based on Interval Ratio Feriyanto, Erikha; Farikhin, Farikhin; Prima Puspita, Nikken
Jurnal sosial dan sains Vol. 4 No. 3 (2024): Junral Sosial dan Sains
Publisher : Green Publisher Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.59188/jurnalsosains.v4i3.1248

Abstract

Background: One forecasting method that is often used is time series forecasting. The development of applied mathematics has encouraged new mathematical findings that led to the birth of new branches of mathematics, one of which is fuzzy. Purpose: The objectives of the study, namely forecasting, fuzzy set, time series, fuzzy time series, fuzzy time series Singh, interval ratio and measurement of accuracy level. Method: This research method applies Chen's fuzzy time series in the section of determining the universe of talk you to the fuzzification of historical data and in the part of forecasting results obtained through a heuristic approach by building three forecasting rules, namely Rule 2.1, Rule 2.2, and Rule 2.3 to obtain better results and affect very small AFER values. As well as making modifications to the interval partition section using interval ratios to be able to reflect data variations. Results: Based on the calculation of AFER values for order 2, order 3, and order 4 respectively obtained at 1.06389%, 0.689368%, and 0.711947%. Therefore, it can be said, Singh's fuzzy time series forecasting method based on the ratio of 3rd-order intervals is better than that of 2nd-order and 4th-order. Conclusion: Based on the results of research and discussion that has been carried out, it can be concluded that Singh's fuzzy time series forecasting method has the same algorithm as fuzzy time series forecasting. Singh's fuzzy time series forecasting method based on interval ratios applies fuzzy time series and Singh forecasting. Singh's fuzzy time series forecasting modification accuracy rate based on interval ratios produces excellent forecasting values according to evaluator average forecasting error rate (AFER).
Co-Authors 'Aliyah, Dheva Ufiz Adillah, Aisyah Nur Agung, Nadiva Putri Alfiana, Shinta Nur Alhusna, Lathifatul Inayah Aris Puji Widodo Azarine, Dinda Bambang Irawanto Berlian Arswendo Adietya Budi Surodjo Budi Surodjo Cahyo, Yassin Dwi Damayanti, Athalia Dwi Lestari Eminugroho Ratna Sari Feriyanto, Erikha Fitriana Hasnani Fitriana Hasnani Fitriani Fitriani Hanifah, Zaqi Afif Harjito - Hasnani, Fitriana Hermawati, Dinda Widya Ikhtiyar, Zakaria Bani Indah E Wijayanti Indah Emilia Wijayanti Indah Emilia Wijayanti Juwanda, Farikhin Lucia Ratnasari Meryta Febrilian Fatimah Meryta Febrilian Fatimah, Meryta Febrilian Mudrikah Mudrikah Mudrikah, Mudrikah Mufliha, Azza Nuralesa, Suffi Nurdin Bahtiar Nurhasmadiar Nandini Nurhayati, Neri Nurul Fadhilah Paramita, Arum Qurrotulaini Pradjna Pradipta, Benediktus Panji Rahma, Suhaila Faiza Rakha, Andrea Putra Razis Aji Saputro Redemtus Heru Tjahjana Risti Sokawati Saputro, Razis Aji Sartika Silalahi, Jennifer Evelyn Shabah, Shava Shavia Siti Khabibah Siti Khabibah Sokawati, Risti Suryoto Suryoto ., Suryoto Suryoto Suryoto Thomas, Abdiel Bellamy Titi Udjiani SRRM Titi Udjiani SRRM Utami, Ratna Zakiyya Meilia widowati widowati Yeni Susanti