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- Title
An example of a simple finite-dimensional algebra with no finite basis of identities.
- Authors
Isaev, I.; Kislitsin, A.
- Abstract
The article discusses the construction of finite-dimensional algebra that has no finite basis of identities for an arbitrary finite field F. It demonstrates that L'vov-Kruse theorem within the finite basis of identities in a finite associative ring is not valid for nonassociative ring over a finite field. It mentions the investigation of finite-dimensional simple algebra over an algebraically closed fields that are identified by its identities. It suggests that an identity in the algebra B has been constructed not as a consequence of the finite set of identities.
- Subjects
FINITE fields; DIMENSIONAL analysis; ISOMORPHISM (Mathematics); FINITE differences; INTEGRAL theorems; IDENTITIES (Mathematics); ASSOCIATIVE algebras; NONASSOCIATIVE rings; ASSOCIATIVE rings
- Publication
Doklady Mathematics, 2012, Vol 86, Issue 3, p774
- ISSN
1064-5624
- Publication type
Article
- DOI
10.1134/S1064562412060154