Involutive Residuated Lattices Based on Modular and Distributive Lattices

被引：1
|
作者：
Olson, Jeffrey S. [1 ]
机构：
[1] Norwich Univ, Dept Math, Northfield, VT 05663 USA
来源：
ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS | 2014年 / 31卷 / 03期
关键词：
Involutive residuated lattice; Involution; Modular lattice;
D O I：
10.1007/s11083-013-9307-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
An involutive residuated lattice (IRL) is a lattice-ordered monoid possessing residual operations and a dualizing element. We show that a large class of self-dual lattices may be endowed with an IRL structure, and give examples of lattices which fail to admit IRLs with natural algebraic conditions. A classification of all IRLs based on the modular lattices M-n is provided.
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页码：373 / 389
页数：17
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