Pseudo-Commutative Algebras

Hee Sik Kim; J. Neggers; Sun Shin Ahn

doi:10.20944/preprints201810.0486.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 19 October 2018 / Approved: 22 October 2018 / Online: 22 October 2018 (10:04:34 CEST)

In this paper, we investigate the effects of certain variants of the commutative laws on properties of several families of algebras which are in general not commutative, such as groups, linear algebras, or actually quite anti-commutative, such as $BCK$-algebras and $d$-algebras among others. From results obtained it becomes clear that by considering these variants in the presence of yet other axioms it is to be expected that a quite rich and varied set of results may be obtained both in the general and the particular setting of which what has been accomplished in this paper is a substantial sample.

(left-, right-) pseudo-commutative; commutative; d/BCK-algebra; disjoint; (linear) groupoid

Computer Science and Mathematics, Algebra and Number Theory

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Pseudo-Commutative Algebras

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