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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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2007 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут прикладної математики і механіки НАН України
2007
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/152370 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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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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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On sum of a nilpotent and an ideally finitealgebras |
| spellingShingle |
On sum of a nilpotent and an ideally finitealgebras Bilun, S.V. |
| title_short |
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_sort |
on sum of a nilpotent and an ideally finitealgebras |
| author |
Bilun, S.V. |
| author_facet |
Bilun, S.V. |
| publishDate |
2007 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/152370 |
| 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. |
| work_keys_str_mv |
AT bilunsv onsumofanilpotentandanideallyfinitealgebras |
| first_indexed |
2025-12-07T15:28:48Z |
| last_indexed |
2025-12-07T15:28:48Z |
| _version_ |
1850863862351396864 |