Bimultiplications and Annihilators of Crossed Modules in Associative Algebras
Journal of New Theory, no.35, pp.72-90, 2021 (Peer-Reviewed Journal)
- Publication Type: Article / Article
- Publication Date: 2021
- Journal Name: Journal of New Theory
- Page Numbers: pp.72-90
- Eskisehir Osmangazi University Affiliated: Yes
Abstract
In this paper, we present a generalization of the concept of the bimultiplication algebra by defining the bimultiplication of crossed modules in associative
algebras. Using this structure, we construct the actor of a crossed module in associative algebras, and we obtain annihilators of crossed modules as the kernel of a crossed
module morphism from a crossed module to its actor. Moreover, we construct a link
between this morphism and a crossed square, two-dimensional crossed module.