Commutative extended BCK-algebras

Subrahmanyam, N. V.

doi:10.2478/s12175-011-0026-1

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2013

2021

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“…In view of strongly connections with a BIK + -logic, BCC -algebra also is called BIK + -algebra (see [19,26]). Now, such algebras are studied by many authors in many directions (see for example [4,7,8,10,15,20,23,[25][26][27]). …”

Section: Introductionmentioning

confidence: 99%

BCC-algebras and residuated partially-ordered groupoid

Zhang

2013

Mathematica Slovaca

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ABSTRACT. The aim of the paper is to investigate the relationship between BCC -algebras and residuated partially-ordered groupoids. We prove that an integral residuated partially-ordered groupoid is an integral residuated pomonoid if and only if it is a double BCC -algebra. Moreover, we introduce the notion of weakly integral residuated pomonoid, and give a characterization by the notion of pseudo-BCI algebra. Finally, we give a method to construct a weakly integral residuated pomonoid (pseudo-BCI algebra) from any bounded pseudo-BCK algebra with pseudo product and any group.

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