On decomposition of pseudo BL-algebras

Mathematica Slovaca

Tomasz Kowalski¹  Anatolij Dvurečenskij¹ 

关键词: pseudo MV-algebra;    pseudo BL-algebra;    pseudo hoop;    idempotent;    â„“-group;    unital â„“-group;    Wajsberg algebra;   

DOI  :  10.2478/s12175-011-0014-5

学科分类：数学（综合）

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

【 摘 要 】

We show that under some conditions, imposed on coatoms and maximal idempotents of a pseudo BL-algebra, we can decompose a pseudo BL-algebra M as an ordinal sum and we show that then M is linearly ordered. We investigate pseudo BL-algebras with a unique coatom a and with a maximal idempotent, and analyze two main situations: either a n = a n+1 holds for some n ≥ 1, or a n > a n+1 hold for any n ≥ 1. We note that there exist (subdirectly irreducible) algebras with two coatoms that are not linearly ordered, so the restriction to a single coatom is natural.

【 授权许可】

Unknown