On sum of a nilpotent and an ideally finitealgebras

• Published in: Algebra and Discrete Mathematics
• Date: 2007
• Main Author: Bilun, S.V.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2007
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/152370
• 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.

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...