On decomposition of pseudo BL-algebras

✍ Scribed by Anatolij Dvurečenskij; Tomasz Kowalski

• Book ID: 111493153
• Publisher: SP Versita
• Year: 2011
• Tongue: English
• Weight: 235 KB
• Volume: 61
• Category: Article
• ISSN: 0139-9918
• DOI: 10.2478/s12175-011-0014-5

✦ Synopsis

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.