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Properties of Cohereditary Comodule Hanni Garminia; Pudji Astuti; Irawati Irawati
Jurnal Matematika & Sains Vol 12, No 2 (2007)
Publisher : Institut Teknologi Bandung

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Abstract

Let R be a commutative ring and C be an R-coalgebra which, as an R-module, is locally projective. This article describes some properties of a cohereditary C-comodule. The properties are derived by exploiting the closed connection between the C*-comodule category and the full subcategory of the C*-module category consisting of all C*-subgenerated C*-modules, where C* is the dual algebra of C.
Struktur Modul Hasil Bagi dari Modul Dedekind Hanni Garminia; Pudji Astuti; Irawati Irawati
Jurnal Matematika & Sains Vol 13, No 4 (2008)
Publisher : Institut Teknologi Bandung

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Abstract

It is well known that the quotient ring of a Dedekind prime ring is a Dedekind prime ring. In this article we generalize the property of Dedekind ring to a module over a commutative ring. Particularly we show that the quotient module of a Dedekind module is a Dedekind module.
Auslander Reiten Quiver of Nakayama Algebra Nn-2,n Faisal Faisal; Irawati Irawati; Intan Muchtadi Alamsyah
Jurnal Matematika & Sains Vol 18, No 1 (2013)
Publisher : Institut Teknologi Bandung

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Abstract

For an algebraically closed field K, given a finite dimensional K-algebra A of  finite representation-type, we can store all the information of the module category mod A by its Auslander Reiten quiver of mod A. In this paper, we will determine the Auslander Reiten quiver of Nakayama algebra Nn-2,n  for every natural number n greater than or equal to 3, that is the  Nakayama algebra KQ/I where Q is a linear orientation cyclic quiver with  vertices and  denotes the ideal of the path algebra KQ generated by the paths of length of n – 1. Keywords: AR-quiver , Nakayama algebra, Quiver.   Quiver Auslander Reiten dari Aljabar Nakayama Nn-2,n AbstrakDiberikan K-aljabar A berdimensi hingga tipe representasi hingga dengan K suatu lapangan yang tertutup secara aljabar,  kita dapat menyimpan semua informasi dari kategori modul kanan mod A menggunakan Auslander Reiten quiver (AR-quiver) dari mod A. Dalam artikel ini, kita akan menentukan quiver Auslander Reiten dari aljabar Nakayama untuk setiap bilangan asli n lebih besar sama dengan 3. Aljabar Nn-2,n adalah aljabar Nakayama KQ/I dimana Q adalah quiver siklis berorientasi linier dengan  titik dan I adalah ideal dari aljabar lintasan KQ yang dibangun oleh lintasan panjang n – 1. Kata Kunci : AR-quiver, Aljabar Nakayama, Quiver.
Jumlah Langsung Subsemimodul Prima Andi Muhammad Anwar; Hanni Garminia; Irawati Irawati
Jurnal Matematika, Statistika dan Komputasi Vol. 18 No. 2 (2022): JANUARY 2022
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/j.v18i2.16669

Abstract

Let be a commutative semiring. A semimodule over a semiring is a fully prime semimodule if each proper subsemimodule of is prime. This research aims to investigate the relationship between a direct sum of prime subsemimodules and , , and a fully prime semimodule.
Auslander Reiten Quiver of Nakayama Algebra type Dynkin Graph An Faisal Anwar; I. Irawati; Intan Muchtadi-Alamsyah
Journal of Mathematical and Fundamental Sciences Vol. 45 No. 1 (2013)
Publisher : Institute for Research and Community Services (LPPM) ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/j.math.fund.sci.2013.45.1.1

Abstract

In this paper we will determine Auslander Reiten quiver of Nakayama algebra with quiver type Dynkin graph An for all natural number n ≥ 2. The AR-quiver is a visualization of module category of finite dimensional algebras. From the AR-quiver of an algebra A we may know all the isomorphism classes of indecomposable modules in mod A and the homomorphism between them. Once we get the general shape of the AR-quiver of this algebra, we will use it to compute a tilting module of this algebra.
CHARACTERIZATION OF WEAKLY PRIME SUBMODULE Puspa Nur Afifah; Irawati Irawati
Journal of Fundamental Mathematics and Applications (JFMA) Vol 4, No 2 (2021)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (913.039 KB) | DOI: 10.14710/jfma.v4i2.12189

Abstract

Let R is a commutative ring with identity and M is a unital R-module. El-bast and Smith (1988) have researched and introduced the multiplication module. Prime submodule has been studied by Ameri (2002). Then Atani and Farzalipour (2007) have extended the prime submodule to weakly prime submodule. Some properties were proved on each paper. This paper will study about characterization of weakly prime submodules.
SIFAT KEPRIMAAN MODUL SEDERHANA CHEN UNTUK GRAF ????∞ Risnawita Risnawita; Irawati Irawati; Intan Muchtadi Alamsyah
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 12, No 2 (2018): JURNAL EPSILON VOLUME 12 NOMOR 2
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (222.299 KB) | DOI: 10.20527/epsilon.v12i2.314

Abstract

Let ???????? be a field, ???????? is a directed graph. Let ????????~ is a directed line graph. Suppose that ????????[????????] is a class of Chen simple module for the Leavitt path algebra (???????????????? (????????)), with [p] being equivalent classes containing an infinite path. An infinite path p is an infinite sequence from the sides of a graph. In this paper it will be shown that ????????[????????]is not a prime module of the Leavitt path algebra for graph ????????∞ .Keywords : Leavitt path algebra, Graph ????????~, Chen simple modules, Prime modules
Modul Herediter atas aljabar Lintasan Leavitt dari Graf A∞ Delsi Kariman; Irawati Irawati; Intan Muchtadi-Alamsyah
Jurnal Matematika Integratif Vol 15, No 1: April, 2019
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (332.904 KB) | DOI: 10.24198/jmi.v15.n1.21027.63-68

Abstract

Misalkan E suatu graf berarah dan K lapangan.  Aljabar lintasan Leavitt LK(E) adalah K-aljabar lintasan diperluas yang berasosiasi dengan graf E modulo relasi tertentu.  Dalam tulisan ini, diselidiki sifat keherediteran modul atas aljabar lintasan Leavitt dari graf garis tak hingga A∞.