Congruence Lattices of Semilattices with Operators

被引：6
|
作者：
Hyndman, Jennifer [1 ]
Nation, J. B. [2 ]
Nishida, Joy [2 ]
机构：
[1] Univ No British Columbia, Dept Math, Prince George, BC V2L 5P2, Canada
[2] Univ Hawaii, Dept Math, Honolulu, HI 96822 USA
来源：
STUDIA LOGICA | 2016年 / 104卷 / 02期
关键词：
Congruence lattice; Semilattice; Operator; Duality;
D O I：
10.1007/s11225-015-9641-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The duality between congruence lattices of semilattices, and algebraic subsets of an algebraic lattice, is extended to include semilattices with operators. For a set G of operators on a semilattice S, we have , where L is the ideal lattice of S, and H is a corresponding set of adjoint maps on L. This duality is used to find some representations of lattices as congruence lattices of semilattices with operators. It is also shown that these congruence lattices satisfy the Jnsson-Kiefer property.
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页码：305 / 316
页数：12
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