Bimultiplications and Annihilators of Crossed Modules in Associative Algebras

EGE ARSLAN U., HÜRMETLİ S.

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.