Binary perm algebras and alternative algebras
A. Kunanbayev, B.K. Sartayev

TL;DR
This paper explores the structure of binary perm algebras, a subvariety of alternative algebras, by identifying their defining identities, constructing a basis, and classifying identities under the commutator operation.
Contribution
It introduces the defining identities of binary perm algebras, constructs their free algebra basis, and classifies identities related to the commutator, advancing understanding of this algebraic variety.
Findings
Identified defining identities of binary perm algebras.
Constructed a basis for free binary perm algebras.
Classified identities satisfied under the commutator.
Abstract
In this paper, we describe the defining identities of a variety of binary perm algebras, which is a subvariety of the variety of alternative algebras. In addition, we construct a basis of the free binary perm algebra and find a complete list of identities which satisfy binary perm algebra under commutator.
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Algebra and Logic · Algebraic structures and combinatorial models
