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 ∈ R such that aR=bR there exist neat elements s,t∈R such th...

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Published in:Algebra and Discrete Mathematics
Date:2015
Main Authors: Pihura, O., Zabavsky, B.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2015
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/155168
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:A morphic ring of neat range one / O. Pihura, B. Zabavsky // Algebra and Discrete Mathematics. — 2015. — Vol. 20, № 2. — С. 325-329. — Бібліогр.: 10 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Pihura, O.
Zabavsky, B.
author_facet Pihura, O.
Zabavsky, B.
citation_txt A morphic ring of neat range one / O. Pihura, B. Zabavsky // Algebra and Discrete Mathematics. — 2015. — Vol. 20, № 2. — С. 325-329. — Бібліогр.: 10 назв. — англ.
collection DSpace DC
container_title Algebra and Discrete Mathematics
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 ∈ R such that aR=bR there exist neat elements s,t∈R such that bs=c, ct=b. Examples of morphic rings of neat range one are given.
first_indexed 2025-12-07T15:53:09Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1726-3255
language English
last_indexed 2025-12-07T15:53:09Z
publishDate 2015
publisher Інститут прикладної математики і механіки НАН України
record_format dspace
spelling Pihura, O.
Zabavsky, B.
2019-06-16T10:09:38Z
2019-06-16T10:09:38Z
2015
A morphic ring of neat range one / O. Pihura, B. Zabavsky // Algebra and Discrete Mathematics. — 2015. — Vol. 20, № 2. — С. 325-329. — Бібліогр.: 10 назв. — англ.
1726-3255
2010 MSC:13F99.
https://nasplib.isofts.kiev.ua/handle/123456789/155168
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 ∈ R such that aR=bR there exist neat elements s,t∈R such that bs=c, ct=b. Examples of morphic rings of neat range one are given.
en
Інститут прикладної математики і механіки НАН України
Algebra and Discrete Mathematics
A morphic ring of neat range one
Article
published earlier
spellingShingle A morphic ring of neat range one
Pihura, O.
Zabavsky, B.
title 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_short A morphic ring of neat range one
title_sort morphic ring of neat range one
url https://nasplib.isofts.kiev.ua/handle/123456789/155168
work_keys_str_mv AT pihurao amorphicringofneatrangeone
AT zabavskyb amorphicringofneatrangeone
AT pihurao morphicringofneatrangeone
AT zabavskyb morphicringofneatrangeone