ON DECOMPOSITION OF PSEUDO BL-ALGEBRAS

被引：8

作者：

Dvurecenskij, Anatolij ^{[1
]}

Kowalski, Tomasz ^{[2
]}

机构：

[1] Slovak Acad Sci, Math Inst, SK-81473 Bratislava, Slovakia

[2] Univ Cagliari, Fac Sci Filosof & Pedag, I-09123 Cagliari, Italy

来源：

MATHEMATICA SLOVACA | 2011年 / 61卷 / 03期

关键词：

pseudo MV-algebra; pseudo BL-algebra; pseudo hoop; idempotent; l-group; unital l-group; Wa[!text type='js']js[!/text]berg algebra; VARIETIES;

D O I：

10.2478/s12175-011-0014-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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 idem-potent, 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. (C) 2011 Mathematical Institute Slovak Academy of Sciences

引用

页码：307 / 326

页数：20

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