Splitting Extensions of Nonassociative Algebras and Modules with Metagroup Relations

Abstract

A class of nonassociative algebras is investigated with mild relations induced from metagroup structures. Modules over nonassociative algebras are studied. For a class of modules over nonassociative algebras, their extensions and splitting extensions are scrutinized. For this purpose tensor products of modules and induced modules over nonassociative algebras are investigated. Moreover, a developed cohomology theory on them is used.

Keywords

• algebra
• nonassociative
• separable
• ideal
• cohomology
• tensor product