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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

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✦ 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.


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