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Volume 11
Issue 3
10.3390/axioms11030131
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Article

Splitting Extensions of Nonassociative Algebras and Modules with Metagroup Relations

by
Sergey Victor Ludkowski
Department of Applied Mathematics, MIREA—Russian Technological University, Av. Vernadsky 78, 119454 Moscow, Russia
Axioms 2022, 11(3), 131; https://doi.org/10.3390/axioms11030131
Submission received: 4 February 2022 / Revised: 28 February 2022 / Accepted: 1 March 2022 / Published: 14 March 2022
(This article belongs to the Special Issue Algebra, Logic and Applications)
Versions Notes

Abstract

A class of nonassociative algebras is investigated with mild relations induced from metagroup structures. Modules over nonassociative algebras are studied. For a class of modules over nonassociative algebras, their extensions and splitting extensions are scrutinized. For this purpose tensor products of modules and induced modules over nonassociative algebras are investigated. Moreover, a developed cohomology theory on them is used.
Keywords: algebra; nonassociative; separable; ideal; cohomology; tensor product; gradation algebra; nonassociative; separable; ideal; cohomology; tensor product; gradation

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MDPI and ACS Style

Ludkowski, S.V. Splitting Extensions of Nonassociative Algebras and Modules with Metagroup Relations. Axioms 2022, 11, 131. https://doi.org/10.3390/axioms11030131

AMA Style

Ludkowski SV. Splitting Extensions of Nonassociative Algebras and Modules with Metagroup Relations. Axioms. 2022; 11(3):131. https://doi.org/10.3390/axioms11030131

Chicago/Turabian Style

Ludkowski, Sergey Victor. 2022. "Splitting Extensions of Nonassociative Algebras and Modules with Metagroup Relations" Axioms 11, no. 3: 131. https://doi.org/10.3390/axioms11030131

APA Style

Ludkowski, S. V. (2022). Splitting Extensions of Nonassociative Algebras and Modules with Metagroup Relations. Axioms, 11(3), 131. https://doi.org/10.3390/axioms11030131

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