Bimultiplications and Annihilators of Crossed Modules in Associative Algebras

Authors : Ummahan EGE ARSLAN, Serdar HÜRMETLİ

Pages : 72-90

Doi:10.53570/jnt.905298

View : 14 | Download : 6

Publication Date : 2021-06-30

Article Type : Research Paper

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.
Keywords : Bimultiplication crossed module, actor crossed module, annihilator of crossed module, crossed square