Algebraically closed algebras in certain small congruence distributive varieties

被引：2

作者：

Ouwehand, P. ^{[1
]}

机构：

[1] Univ Stellenbosch, Dept Math Sci, ZA-7600 Stellenbosch, South Africa

来源：

ALGEBRA UNIVERSALIS | 2009年 / 61卷 / 02期

关键词：

Algebraically closed algebras; absolute retracts; amalgamation; congruence distributivity; AMALGAMATION PROPERTY; LATTICE VARIETIES;

D O I：

10.1007/s00012-009-0015-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In a finitely generated congruence distributive variety satisfying a weak congruence extension property, the algebraically closed algebras are precisely up-directed unions of maximal subdirectly irreducibles. The class of algebraically closed algebras of such a variety is elementary and definable by Horn sentences.

引用

页码：247 / 260

页数：14

共 23 条

[1] Banaschewski B., 1972, ALGEBR UNIV, V2, P152
[2] AMALGAMATION CLASSES OF SOME DISTRIBUTIVE VARIETIES
BERGMAN, C
[J]. ALGEBRA UNIVERSALIS, 1985, 20 (02) : 143 - 166
[3] NON-AXIOMATIZABILITY OF THE AMALGAMATION CLASS OF MODULAR LATTICE VARIETIES
BERGMAN, C
[J]. ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 1989, 6 (01): : 49 - 58
[4] ON THE RELATIONSHIP OF AP, RS AND CEP IN CONGRUENCE MODULAR VARIETIES .2.
BERGMAN, C
MCKENZIE, R
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 103 (02) : 335 - 342
[5] AMALGAMATION IN THE PENTAGON VARIETY
BRUYNS, P
NATURMAN, C
ROSE, H
[J]. ALGEBRA UNIVERSALIS, 1992, 29 (03) : 303 - 322
[6] Burris Bur75 S., 1975, Algebra Universalis, V5, P341, DOI [10.1007/BF02485268, DOI 10.1007/BF02485268]
[7] CHANG CC, 1978, STUDIES LOGIC FDN MA, V73
[8] THE AMALGAMATION PROPERTY FOR VARIETIES OF LATTICES
DAY, A
JEZEK, J
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1984, 286 (01) : 251 - 256
[9] Frayne T., 1962, Fundam. Math, V51, P195, DOI DOI 10.4064/FM-51-3-195-228
[10] HODGES W, 1993, ENCY MATH ITS APPL, V423

← 1 2 3 →