On implicative BE algebras

Andrzej Walendziak

Abstract


We consider some generalizations of BCK algebras (RML, BE, aBE, BE** and aBE** algebras). We investigate the property of implicativity for these algebras. We prove that for any implicative BE** algebra the commutativity property is equivalent to the property of antisymmetry and show that implicative aBE** algebras are commutative BCK algebras. We also show that the class of implicative BE** algebras is a variety.

Keywords


BE algebra; BE** algebra; BCK algebra; commutativity; implicativity

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References


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DOI: http://dx.doi.org/10.17951/a.2022.76.2.45-54
Date of publication: 2023-03-13 22:27:58
Date of submission: 2023-03-12 19:20:51


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