On sum of a nilpotent and an ideally finitealgebras
We study associative algebras R over arbitrary fields which can be decomposed into a sum R=A+B of their subalgebras A and B such that A²=0 and B is ideally finite (is a sum of its finite dimensional ideals). We prove that R has a locally nilpotent ideal I such that R/I is an extension of ideally fin...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2007 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2007
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/152370 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On sum of a nilpotent and an ideally finitealgebras / S.V. Bilun // Algebra and Discrete Mathematics. — 2007. — Vol. 6, № 3. — С. 38–45. — Бібліогр.: 7 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862669451060576256 |
|---|---|
| author | Bilun, S.V. |
| author_facet | Bilun, S.V. |
| citation_txt | On sum of a nilpotent and an ideally finitealgebras / S.V. Bilun // Algebra and Discrete Mathematics. — 2007. — Vol. 6, № 3. — С. 38–45. — Бібліогр.: 7 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | We study associative algebras R over arbitrary fields which can be decomposed into a sum R=A+B of their subalgebras A and B such that A²=0 and B is ideally finite (is a sum of its finite dimensional ideals). We prove that R has a locally nilpotent ideal I such that R/I is an extension of ideally finite algebra by a nilpotent algebra. Some properties of ideally finite algebras are also established.
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| first_indexed | 2025-12-07T15:28:48Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-152370 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T15:28:48Z |
| publishDate | 2007 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Bilun, S.V. 2019-06-10T14:54:53Z 2019-06-10T14:54:53Z 2007 On sum of a nilpotent and an ideally finitealgebras / S.V. Bilun // Algebra and Discrete Mathematics. — 2007. — Vol. 6, № 3. — С. 38–45. — Бібліогр.: 7 назв. — англ. 1726-3255 2000 Mathematics Subject Classification:16N40. https://nasplib.isofts.kiev.ua/handle/123456789/152370 We study associative algebras R over arbitrary fields which can be decomposed into a sum R=A+B of their subalgebras A and B such that A²=0 and B is ideally finite (is a sum of its finite dimensional ideals). We prove that R has a locally nilpotent ideal I such that R/I is an extension of ideally finite algebra by a nilpotent algebra. Some properties of ideally finite algebras are also established. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On sum of a nilpotent and an ideally finitealgebras Article published earlier |
| spellingShingle | On sum of a nilpotent and an ideally finitealgebras Bilun, S.V. |
| title | On sum of a nilpotent and an ideally finitealgebras |
| title_full | On sum of a nilpotent and an ideally finitealgebras |
| title_fullStr | On sum of a nilpotent and an ideally finitealgebras |
| title_full_unstemmed | On sum of a nilpotent and an ideally finitealgebras |
| title_short | On sum of a nilpotent and an ideally finitealgebras |
| title_sort | on sum of a nilpotent and an ideally finitealgebras |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/152370 |
| work_keys_str_mv | AT bilunsv onsumofanilpotentandanideallyfinitealgebras |