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- Title
On Diagonal Nonconstant Right-Symmetric Algebras of Matrix Type.
- Authors
Pozhidaev, A. P.
- Abstract
We describe the right-symmetric algebras of matrix type over a field of characteristic such that the left action of the orthogonal idempotents of is diagonalizable, and the right-module part includes no constant bichains. We construct some wide class of nonassociative algebras , where is a subalgebra and a right module over an associative algebra . We give a criterion for these algebras to be right-symmetric. Assuming that , we show that the algebras of this class are either simple or local. We exhibit some examples of simple right-symmetric algebras and right-symmetric algebras without nilpotent right ideals whose right-module part is not an irreducible module over .
- Subjects
MATRICES (Mathematics); ASSOCIATIVE algebras; IDEMPOTENTS; SYMMETRIC matrices; ALGEBRA; NONASSOCIATIVE algebras
- Publication
Siberian Mathematical Journal, 2023, Vol 64, Issue 4, p879
- ISSN
0037-4466
- Publication type
Article
- DOI
10.1134/S0037446623040109