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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| Veröffentlicht in: | Algebra and Discrete Mathematics |
|---|---|
| Datum: | 2015 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2015
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/155168 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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| _version_ | 1862682500521787392 |
|---|---|
| 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.
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| first_indexed | 2025-12-07T15:53:09Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-155168 |
| 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 |