Dian Winda Setyawati
Jurusan Matematika FMIPA Institut Teknologi Sepuluh Nopember

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Derivation Requirements on Prime Near-Rings for Commutative Rings Setyawati, Dian Winda; Habibi, Mochammad Reza; Baihaqi, Komar
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.
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.
PRIME IDEAL ON SEMIRINGS D_nxn (Z^+) Setyawati, Dian Winda
MATEMATIKA Vol 14, No 1 (2011): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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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
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.