Ideal and factor conditions for crossed modules and algebra-algebroids

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Hacettepe Journal of Mathematics and Statistics
Volume:52 Issue:3
Ideal and factor conditions for crossed modules and algebra-algebroids

Ideal and factor conditions for crossed modules and algebra-algebroids

Authors : Özgün GÜRMEN ALANSAL

Pages : 698-707

Doi:10.15672/hujms.1131802

View : 133 | Download : 184

Publication Date : 2023-05-30

Article Type : Research Paper

Abstract :In this paper, using the equivalence between the category of crossed modules of algebras and the category of algebra-algebroids, we will explore the notions of ideality and factors for these algebraic structures. We give the structure of a two sided ideal of an algebra-algebroid and the notion of quotient algebra-algebroid. By considering a two sided ideal of an algebra-algebroid, we show that the crossed module corresponding to this ideal is a crossed ideal of the crossed module corresponding to the algebra-algebroid. Conversely, by taking a crossed ideal of a crossed module, we also show that the corresponding algebra-algebroid to this crossed ideal is an ideal of the algebra-algebroid corresponding to the crossed module.
Keywords : Algebra Algebroids, category, crossed modules

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