Skew residuated lattices

被引：7

作者：

Chajda, I. ^{[1
]}

Krnavek, J. ^{[1
]}

机构：

[1] Palacky Univ, Fac Sci, Dept Algebra & Geometry, Olomouc 77146, Czech Republic

来源：

FUZZY SETS AND SYSTEMS | 2013年 / 222卷

关键词：

Skew residuated lattice; Adjointness property; Reversion; Difference property; Sectional involution; Divisibility semiloop;

D O I：

10.1016/j.fss.2012.11.019

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We replace the so-called adjointness in the definition of residuated lattice by its strict version where inequalities are replaced by equalities. We prove that such structures, called skew residuated lattices, can be characterized as lattices with certain involutions in principal filters. Since skew residuated lattices have the cancellation property, they are close to divisibility loops introduced by B. Bosbach in 1988. We show the condition under which the skew residuated lattices can be represented by such loops. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：78 / 83

页数：6

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