Isomorphism Theorems for Crossed Squares of Commutative Algebras

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Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi
Volume:28 Issue:2
Isomorphism Theorems for Crossed Squares of Commutative Algebras

Isomorphism Theorems for Crossed Squares of Commutative Algebras

Authors : Selim Çetin, Erkan Can

Pages : 177-188

Doi:10.19113/sdufenbed.1486991

View : 38 | Download : 12

Publication Date : 2024-08-23

Article Type : Research Paper

Abstract :The isomorphism theorems for crossed squares of commutative algebras, which arise when the crossed modules of algebras are given an extra dimension, are the main subject of this paper. The definition of crossed squares of commutative algebras is given in this context, encompassing ideas like the crossed square ideal, image, and quotient crossed squares, as well as the kernel for crossed square morphisms. The study discusses the way how isomorphism theorems are applied to these structures and offers detailed proofs for this framework. Moreover, some necessary concepts such as quotient crossed squares, which were not previously specified in these structures, are also presented, and some basic properties are examined. The study provides opportunities for possible generalization to a number of different structures, including crossed n-cubes.
Keywords : İzomorfizm teoremi, Alt çaprazlanmış kare, Çaprazlanmış kare ideali

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