Bounded commutative residuated ℓ-monoids with general comparability and states

被引：0
|
作者：
A. Dvurečenskij
J. Rachůnek
机构：
[1] Slovak Academy of Sciences,Mathematical Institute
[2] Palacký University,Department of Algebra and Geometry, Faculty of Sciences
来源：
Soft Computing | 2006年 / 10卷
关键词：
Bounded commutative ; ℓ-monoid; general comparability property; Boolean element; State; State-morphism; Extremal state; filter; Maximal filter; MV-algebra; BL-algebra; 06D35; 06F05; 03G25; 03B50; 28E15;
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中图分类号：
学科分类号：
摘要：
Bounded commutative Rℓ-monoids are a generalization of MV-algebras as well as of BL-algebras. For such monoids the authors in [DvRa] introduced states, analogues of probability measures. We study Boolean elements and introduce the general comparability property. It entails that the monoids with the property are BL-algebras, and extremal states on Boolean elements can be uniquely extended to extremal states on the monoids. Moreover, the hull-kernel topology of maximal filters is totally disconnected.
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页码：212 / 218
页数：6
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