- Journal of New Theory
- Issue: 35
- Bimultiplications and Annihilators of Crossed Modules in Associative Algebras
Bimultiplications and Annihilators of Crossed Modules in Associative Algebras
Authors : Ummahan Ege Arslan, Serdar Hürmetli
Pages : 72-90
Doi:10.53570/jnt.905298
View : 15 | Download : 5
Publication Date : 2021-06-30
Article Type : Research
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