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Journals / Journal of New Theory / 2021 / Cilt: 2021 - Sayı: 35

Bimultiplications and Annihilators of Crossed Modules in Associative Algebras

Ummahan EGE ARSLAN
Serdar HÜRMETLİ
Pages
72–90
Publication Date
2022-10-19
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Moreover, we construct a link between this morphism and a crossed square, two-dimensional crossed module.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we present a generalization of the concept of the bimultiplication algebra by defining the bimultiplication of crossed modules in associative algebras.
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Key Findings & Data: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.
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Conclusion & Impact:Moreover, we construct a link between this morphism and a crossed square, two-dimensional crossed module.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Bimultiplication crossed module · actor crossed module · annihilator of crossed module

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.

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Cite This Article

ARSLAN, U. E., HÜRMETLİ, S. (2022). Bimultiplications and Annihilators of Crossed Modules in Associative Algebras. Journal of New Theory, Cilt: 2021 - Sayı: 35, 72–90. https://ajindex.com/articles/565752

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