Indecomposable and irreducible \(t\)-monomial matrices over commutative rings

Indecomposable and irreducible \(t\)-monomial matrices over commutative rings

We introduce the notion of the defining  sequence of a permutation  indecomposable  monomial matrix over a commutative ring and obtain   necessary conditions for such matrices to be indecomposable or irreducible in terms of this sequence.

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Bibliographic Details
Date:2016
Main Authors: Bondarenko, Vitaliy Mykhaylovych, Bortos, Maria, Dinis, Ruslana, Tylyshchak, Alexander
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2016
Subjects:
local ring
similarity
indecomposable matrix
irreducible matrix
canonically \(t\)-cyclic matrix
defining sequence
group
representation
15B33
15A30
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/287
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
id admjournalluguniveduua-article-287
record_format ojs
spelling admjournalluguniveduua-article-2872016-11-15T13:03:03Z Indecomposable and irreducible \(t\)-monomial matrices over commutative rings Bondarenko, Vitaliy Mykhaylovych Bortos, Maria Dinis, Ruslana Tylyshchak, Alexander local ring, similarity, indecomposable matrix, irreducible matrix, canonically \(t\)-cyclic matrix, defining sequence, group, representation 15B33, 15A30 We introduce the notion of the defining  sequence of a permutation  indecomposable  monomial matrix over a commutative ring and obtain   necessary conditions for such matrices to be indecomposable or irreducible in terms of this sequence. Lugansk National Taras Shevchenko University 2016-11-15 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/287 Algebra and Discrete Mathematics; Vol 22, No 1 (2016) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/287/pdf Copyright (c) 2016 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2016-11-15T13:03:03Z
collection OJS
language English
topic local ring
similarity
indecomposable matrix
irreducible matrix
canonically \(t\)-cyclic matrix
defining sequence
group
representation
15B33
15A30
spellingShingle local ring
similarity
indecomposable matrix
irreducible matrix
canonically \(t\)-cyclic matrix
defining sequence
group
representation
15B33
15A30
Bondarenko, Vitaliy Mykhaylovych
Bortos, Maria
Dinis, Ruslana
Tylyshchak, Alexander
Indecomposable and irreducible \(t\)-monomial matrices over commutative rings
topic_facet local ring
similarity
indecomposable matrix
irreducible matrix
canonically \(t\)-cyclic matrix
defining sequence
group
representation
15B33
15A30
format Article
author Bondarenko, Vitaliy Mykhaylovych
Bortos, Maria
Dinis, Ruslana
Tylyshchak, Alexander
author_facet Bondarenko, Vitaliy Mykhaylovych
Bortos, Maria
Dinis, Ruslana
Tylyshchak, Alexander
author_sort Bondarenko, Vitaliy Mykhaylovych
title Indecomposable and irreducible \(t\)-monomial matrices over commutative rings
title_short Indecomposable and irreducible \(t\)-monomial matrices over commutative rings
title_full Indecomposable and irreducible \(t\)-monomial matrices over commutative rings
title_fullStr Indecomposable and irreducible \(t\)-monomial matrices over commutative rings
title_full_unstemmed Indecomposable and irreducible \(t\)-monomial matrices over commutative rings
title_sort indecomposable and irreducible \(t\)-monomial matrices over commutative rings
description We introduce the notion of the defining  sequence of a permutation  indecomposable  monomial matrix over a commutative ring and obtain   necessary conditions for such matrices to be indecomposable or irreducible in terms of this sequence.
publisher Lugansk National Taras Shevchenko University
publishDate 2016
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/287
work_keys_str_mv AT bondarenkovitaliymykhaylovych indecomposableandirreducibletmonomialmatricesovercommutativerings
AT bortosmaria indecomposableandirreducibletmonomialmatricesovercommutativerings
AT dinisruslana indecomposableandirreducibletmonomialmatricesovercommutativerings
AT tylyshchakalexander indecomposableandirreducibletmonomialmatricesovercommutativerings
first_indexed 2025-12-02T15:31:30Z
last_indexed 2025-12-02T15:31:30Z
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