Bricks and pseudo MV-algebras are equivalent

Mathematica Slovaca

N. Subrahmanyam¹ 

关键词: pseudo MV-algebra;    brick;    cone algebra;    â„“-group;    pMV implication;   

DOI  :  10.2478/s12175-008-0061-8

学科分类：数学（综合）

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

【 摘 要 】

We will show that the bricks (of Bosbach) and the pseudo MV-algebras are each term equivalent to the class of semigroups with a pair of unary operations ^ and ˘ satisfying the equations: (âa)^b = b = b(aă)˘ and a($$hat b$$ a)˘ = (bă)^b and also show that a brick is an interval [0, u] of the positive cone of a unital lattice ordered group. We further extend the notion of implications to a pseudo MV-algebra and study the algebra of such implications.

【 授权许可】

Unknown