Local pseudo-BCK algebras with pseudo-product

Mathematica Slovaca

Lavinia Ciungu¹ 

关键词: pseudo-BCK algebra;    deductive system;    local pseudo-BCK(pP) algebra;    good pseudo-BCK(pP) algebra;    maximal deductive system;    normal deductive system;    primary deductive system;    perfect pseudo-BCK(pP) algebra;    radical;   

DOI  :  10.2478/s12175-011-0001-x

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

Pseudo-BCK algebras were introduced by G. Georgescu and A. Iorgulescu as a generalization of BCK algebras in order to give a corresponding structure to pseudo-MV algebras, since the bounded commutative BCK algebras correspond to MV algebras. Properties of pseudo-BCK algebras and their connections with other fuzzy structures were established by A. Iorgulescu and J. Kühr. The aim of this paper is to define and study the local pseudo-BCK algebras with pseudo-product. We will also introduce the notion of perfect pseudo-BCK algebras with pseudo-product and we will study their properties. We define the radical of a bounded pseudo-BCK algebra with pseudo-product and we prove that it is a normal deductive system. Another result consists of proving that every strongly simple pseudo-hoop is a local bounded pseudo-BCK algebra with pseudo-product.

【 授权许可】

Unknown