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.

引用

页码：305 / 316

页数：12

共 14 条

[1] The Jónsson-Kiefer property
Adaricheva K.
McKenzie R.
Zenk E.R.
Maróti M.
Nation J.B.
[J]. Studia Logica, 2006, 83 (1-3) : 111 - 131
[2] ADARICHEVA K., 2012, INT J ALGEBR COMPUT, V22, pN7
[3] [Anonymous], 1964, Journal of the London Mathematical Society
[4] [Anonymous], 1982, T I MAT SO AN SSSR
[5] Natural dualities for semilattice-based algebras
Davey, B. A.
Jackson, M.
Pitkethly, J. G.
Talukder, M. R.
[J]. ALGEBRA UNIVERSALIS, 2007, 57 (04) : 463 - 490
[6] FAJTLOWICZ S., 1976, C MATH SOC JANOS BOL, V14, P51
[7] CONGRUENCE LATTICES OF SEMILATTICES
FREESE, R
NATION, JB
[J]. PACIFIC JOURNAL OF MATHEMATICS, 1973, 49 (01) : 51 - 58
[8] GORBUNOV V, 1998, ALGEBRAIC THEORY QUA
[9] THE STRUCTURE OF THE LATTICES OF QUASIVARIETIES
GORBUNOV, VA
[J]. ALGEBRA UNIVERSALIS, 1994, 32 (04) : 493 - 530
[10] HOEHNKE H.-J., 1983, C MATH SOC JANOS BOL, V43, P189

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