Ideal and factor conditions for crossed modules and algebra-algebroids

Year 2023, Volume: 52 Issue: 3, 698 - 707, 30.05.2023

Özgün Gürmen Alansal

https://doi.org/10.15672/hujms.1131802

Cited By: 1

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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