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A morphic ring of neat range one

A morphic ring of neat range one

We show that a commutative ring \(R\) has neat range one if and only if every unit modulo principal ideal of a ring lifts to a neat element. We also show that a commutative morphic ring \(R\) has a neat range one if and only if for any elements \(a, b \in R\) such that \(aR=bR\) there exist neat ele...

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Main Authors: Pihura, Oksana, Zabavsky, Bohdan
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2016
Subjects:
Bezout ring
neat ring
clear ring
elementary divisor ring
stable range one
neat range one
13F99
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/57
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spelling oai:ojs.admjournal.luguniv.edu.ua:article-572016-01-12T07:40:37Z A morphic ring of neat range one Pihura, Oksana Zabavsky, Bohdan Bezout ring, neat ring, clear ring, elementary divisor ring, stable range one, neat range one 13F99 We show that a commutative ring \(R\) has neat range one if and only if every unit modulo principal ideal of a ring lifts to a neat element. We also show that a commutative morphic ring \(R\) has a neat range one if and only if for any elements \(a, b \in R\) such that \(aR=bR\) there exist neat elements \(s, t \in R\) such that \(bs=c\), \(ct=b\). Examples of morphic rings of neat range one are given. Lugansk National Taras Shevchenko University 2016-01-12 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/57 Algebra and Discrete Mathematics; Vol 20, No 2 (2015) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/57/pdf Copyright (c) 2016 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
collection OJS
language English
topic Bezout ring
neat ring
clear ring
elementary divisor ring
stable range one
neat range one
13F99
spellingShingle Bezout ring
neat ring
clear ring
elementary divisor ring
stable range one
neat range one
13F99
Pihura, Oksana
Zabavsky, Bohdan
A morphic ring of neat range one
topic_facet Bezout ring
neat ring
clear ring
elementary divisor ring
stable range one
neat range one
13F99
format Article
author Pihura, Oksana
Zabavsky, Bohdan
author_facet Pihura, Oksana
Zabavsky, Bohdan
author_sort Pihura, Oksana
title A morphic ring of neat range one
title_short A morphic ring of neat range one
title_full A morphic ring of neat range one
title_fullStr A morphic ring of neat range one
title_full_unstemmed A morphic ring of neat range one
title_sort morphic ring of neat range one
description We show that a commutative ring \(R\) has neat range one if and only if every unit modulo principal ideal of a ring lifts to a neat element. We also show that a commutative morphic ring \(R\) has a neat range one if and only if for any elements \(a, b \in R\) such that \(aR=bR\) there exist neat elements \(s, t \in R\) such that \(bs=c\), \(ct=b\). Examples of morphic rings of neat range one are given.
publisher Lugansk National Taras Shevchenko University
publishDate 2016
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/57
work_keys_str_mv AT pihuraoksana amorphicringofneatrangeone
AT zabavskybohdan amorphicringofneatrangeone
AT pihuraoksana morphicringofneatrangeone
AT zabavskybohdan morphicringofneatrangeone
first_indexed 2024-04-12T06:26:12Z
last_indexed 2024-04-12T06:26:12Z
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