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All Journal MATEMATIKA Jurnal Ilmu Dasar Jurnal Sains dan Seni ITS UNEJ e-Proceeding Limits: Journal of Mathematics and Its Applications Sains & Matematika
Dian Winda Setyawati
Jurusan Matematika FMIPA Institut Teknologi Sepuluh Nopember
Arts Humanities Astronomy Biochemistry, Genetics & Molecular Biology Chemistry Control & Systems Engineering Education Mathematics Physics

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 1 
PRIME IDEAL ON SEMIRINGS D_nxn (Z^+) Setyawati, Dian Winda
MATEMATIKA Vol 14, No 1 (2011): JURNAL MATEMATIKA
Publisher : MATEMATIKA

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (69.991 KB)

Abstract

Let R be a semirings. A subset I of R is called an ideal of R if and then and I is called prime ideal if  for  then or  On semirings ,  a non zero ideal I is prime if and only if  , for p is prime or I = <2,3>. A paper will show form of prime ideal of semirings
MATRIKS JORDAN DAN APLIKASINYA PADA SISTEM LINIER WAKTU DISKRIT ., Soleha; Setyawati, Dian Winda
MATEMATIKA Vol 15, No 1 (2012): JURNAL MATEMATIKA
Publisher : MATEMATIKA

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (81.766 KB)

Abstract

Matrix is diagonalizable (similar with matrix diagonal) if and only if the sum of geometric multiplicities of its eigenvalues is n.If we search for an upper triangular form that is nearly diagonal as possible but is still attainable by similarity for every matrix, especially the sum of geometric multiplicities of its eigenvalues is less than n, the result is the Jordan canonical form, which is denoted by , and . In this paper, will be described how to get matrix S(in order to get matrix ) by using generalized eigenvector. In addition, it will also describe the Jordan canonical form and its properties, and some observation and application on discrete time linear system.
BENTUK-BENTUK IDEAL PADA SEMIRING (Z+, +,.) DAN SEMIRING (Z+, ⊕, *) Setyawati, Dian Winda; Soleha, Soleha; Rimadhany, Ruzika
Sains & Matematika Vol 3, No 1 (2014): Oktober, Sains & Matematika
Publisher : Sains & Matematika

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Abstract

Himpunan bilangan bulat taknegatif, yaitu (Z+,+,.) merupakan semiring terhadap operasi penjumlahan dan perkalian biasa, sedangkan himpunan (Z+,?,*) juga merupakan semiring terhadap operasi penjumlahan ? dan perkalian yang didefi nisikan sebagai berikut: untuk setiap a,b?Z+ berlaku a ? b=FPB(a,b) dan a*b=KPK(a,b). Pada semiring R, himpunan bagian I dari R disebut ideal pada R jika a,b ? I dan r ? R maka a+b ? I dan ra, ar ? I . Pada artikel ini ditunjukkan bentukbentuk ideal pada semiring (Z+,+,.) dan bentuk-bentuk ideal pada semiring (Z+,?,*) serta menunjukkan hubungan satu ideal dengan ideal yang lain. Bentuk-bentuk ideal yang ditunjukkan adalah ideal maksimal, ideal substraktif, Q-ideal, ideal prima, ideal semiprima dan ideal primary. The set of nonnegative integers (Z+,+,.) is a semiring of the usual operations of addition and multiplication otherwise set (Z+,?,*) is also a semiring of the addition operation ? and multiplication defi ned as follows: for each a,b?Z+applies a ? b=gcd(a,b) and a*b=lcm(a,b). At semiring R, a subset I of Ris called an ideal in R if a,b ? I and r ? R, then a+b ? I and ra, ar ? I In this paper will be shown the forms of the ideal on the semiring (Z+,+,.) and forms of the ideal on the semiring (Z+,?,*) and shows the relationship of the ideal with the other ideal. Ideal form sthat will be shown is the maximal ideal, substractive ideal, Q-ideal, prime ideal, and the semiprime ideal and, primary ideal.
Bentuk-bentuk Ideal pada Semiring (Z+, +,.) dan Semiring (Z+, ⊕, *) Setyawati, Dian Winda; Soleha, Soleha; Rimadhany, Ruzika
Sains & Matematika Vol 3, No 1 (2014): Oktober, Sains & Matematika
Publisher : Sains & Matematika

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

Abstract

Himpunan bilangan bulat taknegatif, yaitu (Z+,+,.) merupakan semiring terhadap operasi penjumlahan dan perkalian biasa, sedangkan himpunan (Z+,⊕,*) juga merupakan semiring terhadap operasi penjumlahan ⊕ dan perkalian yang didefi nisikan sebagai berikut: untuk setiap a,b∈Z+ berlaku a ⊕ b=FPB(a,b) dan a*b=KPK(a,b). Pada semiring R, himpunan bagian I dari R disebut ideal pada R jika a,b ∈ I dan r ∈ R maka a+b ∈ I dan ra, ar ∈ I . Pada artikel ini ditunjukkan bentukbentuk ideal pada semiring (Z+,+,.) dan bentuk-bentuk ideal pada semiring (Z+,⊕,*) serta menunjukkan hubungan satu ideal dengan ideal yang lain. Bentuk-bentuk ideal yang ditunjukkan adalah ideal maksimal, ideal substraktif, Q-ideal, ideal prima, ideal semiprima dan ideal primary. The set of nonnegative integers (Z+,+,.) is a semiring of the usual operations of addition and multiplication otherwise set (Z+,⊕,*) is also a semiring of the addition operation ⊕ and multiplication defi ned as follows: for each a,b∈Z+applies a ⊕ b=gcd(a,b) and a*b=lcm(a,b). At semiring R, a subset I of Ris called an ideal in R if a,b ∈ I and r ∈ R, then a+b ∈ I and ra, ar ∈ I In this paper will be shown the forms of the ideal on the semiring (Z+,+,.) and forms of the ideal on the semiring (Z+,⊕,*) and shows the relationship of the ideal with the other ideal. Ideal form sthat will be shown is the maximal ideal, substractive ideal, Q-ideal, prime ideal, and the semiprime ideal and, primary ideal.
Kajian Teori Ideal Perluasan Subtraktif Pada Semiring Ternari Nur Qomariah; Dian Winda Setyawati
Jurnal Sains dan Seni ITS Vol 6, No 1 (2017)
Publisher : Lembaga Penelitian dan Pengabdian Kepada Masyarakat (LPPM), ITS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/j23373520.v6i1.21161

Abstract

Pembahasan mengenai teori ideal terus berkembang, salah satunya adalah teori ideal pada semiring ternari. Pada jurnal ini, dikaji mengenai karakteristik ideal-ideal pada semiring ternari Z_0^-×Z_0^- yaitu ideal utama, Q-ideal, ideal subtraktif, dan ideal perluasan subtraktif. Bentuk-bentuk ideal tersebut memiliki hubungan dengan bentuk-bentuk ideal pada semiring Z_0^+×Z_0^+. Selanjutnya dengan menggunakan keterkaitan antara ideal perluasan subtraktif dengan Q-ideal, maka juga dikaji mengenai ideal perluasan subtraktif terkecil pada semiring ternari. Selain itu, juga dikaji mengenai ideal prima pada semiring ternari terhadap semiring ternari faktor.
Derivation Requirements on Prime Near-Rings for Commutative Rings Dian Winda Setyawati; Mochammad Reza Habibi; Komar Baihaqi
Jurnal ILMU DASAR Vol 20 No 2 (2019)
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (761.168 KB) | DOI: 10.19184/jid.v20i2.10297

Abstract

Near-ring is an extension of ring without having to fulfill a commutative of the addition operations and left distributive of the addition and multiplication operations It has been found that some theorems related to a prime near-rings are commutative rings involving the derivation of the Lie products and the derivation of the Jordan product. The contribution of this paper is developing the previous theorem by inserting derivations to the Lie products and the Jordan product. Keywords: Derivation, Prime Near-Ring, Lie Products and Jordan Products.
Teori Ideal Pada Semiring Faktor dan Semiring Ternary Faktor Dian Winda Setyawati
Limits: Journal of Mathematics and Its Applications Vol 14, No 1 (2017)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (663.201 KB) | DOI: 10.12962/limits.v14i1.2209

Abstract

Semiring merupakan generalisasi dari ring dimana syarat invers terhadap penjumlahan dihilangkan. Pada semiring, operasi yang digunakan adalah operasi biner penjumlahan dan operasi  biner perkalian sedangkan pada  semiring ternary, operasi yang digunakan adalah operasi biner penjumlahan dan operasi  terner perkalian. Telah diperoleh karakterisasi ideal, ideal perluasan subtraktif, ideal prima pada semiring factor maupun semiring ternary factor. Pada paper ini akan diberikan pembuktian pada karakterisasi ideal, ideal perluasan subtraktif, ideal prima pada semiring ternary factor dengan mengkaitkan dengan hasil yang telah diperoleh terlebih dahulu pada semiring factor
Bentuk-bentuk Ideal pada Semiring (Z+, +,.) dan Semiring (Z+, ⊕, *) Dian Winda Setyawati; Soleha Soleha; Ruzika Rimadhany
Sains dan Matematika Vol. 3 No. 1 (2014): Oktober, Sains & Matematika
Publisher : Universitas Negeri Surabaya

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

Abstract

Himpunan bilangan bulat taknegatif, yaitu (Z+,+,.) merupakan semiring terhadap operasi penjumlahan dan perkalian biasa, sedangkan himpunan (Z+,⊕,*) juga merupakan semiring terhadap operasi penjumlahan ⊕ dan perkalian yang didefi nisikan sebagai berikut: untuk setiap a,b∈Z+ berlaku a ⊕ b=FPB(a,b) dan a*b=KPK(a,b). Pada semiring R, himpunan bagian I dari R disebut ideal pada R jika a,b ∈ I dan r ∈ R maka a+b ∈ I dan ra, ar ∈ I . Pada artikel ini ditunjukkan bentukbentuk ideal pada semiring (Z+,+,.) dan bentuk-bentuk ideal pada semiring (Z+,⊕,*) serta menunjukkan hubungan satu ideal dengan ideal yang lain. Bentuk-bentuk ideal yang ditunjukkan adalah ideal maksimal, ideal substraktif, Q-ideal, ideal prima, ideal semiprima dan ideal primary. The set of nonnegative integers (Z+,+,.) is a semiring of the usual operations of addition and multiplication otherwise set (Z+,⊕,*) is also a semiring of the addition operation ⊕ and multiplication defi ned as follows: for each a,b∈Z+applies a ⊕ b=gcd(a,b) and a*b=lcm(a,b). At semiring R, a subset I of Ris called an ideal in R if a,b ∈ I and r ∈ R, then a+b ∈ I and ra, ar ∈ I In this paper will be shown the forms of the ideal on the semiring (Z+,+,.) and forms of the ideal on the semiring (Z+,⊕,*) and shows the relationship of the ideal with the other ideal. Ideal form sthat will be shown is the maximal ideal, substractive ideal, Q-ideal, prime ideal, and the semiprime ideal and, primary ideal.
APROKSIMASI PADA GRUP Dian Winda Setyawati; Subiono Subiono
UNEJ e-Proceeding 2022: E-Prosiding Seminar Nasional Matematika, Geometri, Statistika, dan Komputasi (SeNa-MaGeStiK)
Publisher : UPT Penerbitan Universitas Jember

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Abstract

A non-empty set with binary operations on a set is called a group if the set satisfies the associative property, the existence of an identity, and the existence of an inverse for each element of the set . A normal subgroup in group can partition group into equivalence classes so that a lower approximation and an upper approximation can be formed from the non-empty set corresponding to the normal subgroup . Let be a non-empty subset of , the lower approximation of corresponding to the normal subgroup is defined as the set of elements in where the equivalence class of the element is a subset of while the upper approximation of corresponding to the normal subgroup is defined as the set of elements in where the equivalence class of the element intersects the set . In this paper, we will give more general properties regarding the relationship between the upper approximation and the lower approximation by involving two different normal subgroups of group and two different sets that are subsets of group . Furthermore, we will show the corollary of these properties if we use one normal subgroup and one subset of group . Keywords: equivalence classes, lower approximation, upper approximation
Co-Authors Komar Baihaqi Mochammad Reza Habibi Nur Qomariah Rimadhany, Ruzika Ruzika Rimadhany Soleha . Soleha Soleha Soleha Soleha Subiono -