ON MINIMALITY IN PSEUDO-BCI-ALGEBRAS

Title & Authors
ON MINIMALITY IN PSEUDO-BCI-ALGEBRAS
Kim, Young-Hee; So, Keum-Sook;

Abstract
In this paper we consider pseudo-BCK/BCI-algebras. In particular, we consider properties of minimal elements ($\small{x{\leq}a}$ implies x = a) in terms of the binary relation $\small{\leq}$ which is reflexive and anti-symmetric along with several more complicated conditions. Some of the properties of minimal elements obtained bear resemblance to properties of B-algebras in case the algebraic operations $\small{\ast}$ and $\small{\circ}$ are identical, including the property $\small{0{\circ}(0{\ast}a)}$ = a. The condition $\small{0{\ast}(0{\circ}x)=0{\circ}(0{\ast}x)=x}$ all $\small{x{\in}X}$ defines the class of p-semisimple pseudo-BCK/BCI-algebras($\small{0{\leq}x}$ implies x = 0) as an interesting subclass whose further properties are also investigated below.
Keywords
(pseudo-)BCK/BCI-algebra;minimal;p-semisimple;
Language
English
Cited by
1.
Some properties of pseudo-BCK- and pseudo-BCI-algebras, Fuzzy Sets and Systems, 2016
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