This article is cited in 2 papers

Mathematical logic, algebra and number theory

On Mizuhara's construction for endomorphs

A. P. Pozhidaev

Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia

Abstract: We consider Mizuhara's construction for the endomorphs. It is shown that this construction gives almost simple algebras, which are used to construct new examples of simple right-symmetric algebras. To investigate the Mizuhara extensions we give a description of the derivations of the endomorphs constructed on nonunital algebras, which generalizes a result obtained earlier in the unital case.

Keywords: right-symmetric algebra, simple algebra, pre-Lie algebra, Mizuhara's construction, endomorph, derivation.

UDC: 512.57

MSC: 17D20, 17D25, 17A30

Received October 6, 2023, published January 29, 2024

DOI: 10.33048/semi.2024.21.003