Automorphism-primal algebras generate verbose varieties

被引：0

作者：

Bergman, Clifford ^{[1
]}

机构：

[1] Iowa State Univ, Dept Math, Ames, IA 50011 USA

来源：

ALGEBRA UNIVERSALIS | 2015年 / 74卷 / 1-2期

关键词：

verbal congruence; fully invariant congruence; verbose; automorphism-primal; natural duality;

D O I：

10.1007/s00012-015-0337-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A finite algebra is called automorphism-primal if its clone of term operations coincides with all operations that preserve its automorphisms. We prove that the variety generated by an automorphism-primal algebra is verbose, that is, on every member algebra, every fully invariant congruence is verbal. The proof is a nice application of the theory of natural dualities as developed by Davey et al.

引用

页码：117 / 122

页数：6

共 50 条

[1] Automorphism-primal algebras generate verbose varieties
Clifford Bergman
[J]. Algebra universalis, 2015, 74 : 117 - 122
[2] UNIFICATION IN PRIMAL ALGEBRAS, THEIR POWERS AND THEIR VARIETIES
NIPKOW, T
[J]. JOURNAL OF THE ACM, 1990, 37 (04) : 742 - 776
[3] Representations of algebras in varieties generated by infinite primal algebras
Joseph Van Name
[J]. Algebra universalis, 2014, 72 : 201 - 208
[4] Representations of algebras in varieties generated by infinite primal algebras
Van Name, Joseph
[J]. ALGEBRA UNIVERSALIS, 2014, 72 (03) : 201 - 208
[5] Diagram Automorphism Fixed Lie Algebras and Diagram Automorphism Fixed Quiver Varieties
Dong, Zhijie
Ma, Haitao
[J]. FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 2023, 57 (02) : 109 - 116
[6] Diagram Automorphism Fixed Lie Algebras and Diagram Automorphism Fixed Quiver Varieties
Zhijie Dong
Haitao Ma
[J]. Functional Analysis and Its Applications, 2023, 57 : 109 - 116
[7] A note on minimal varieties generated by order-primal algebras
Larose, B
[J]. ALGEBRA UNIVERSALIS, 2003, 49 (01) : 107 - 109
[8] STONE DUALITY FOR VARIETIES GENERATED BY QUASI-PRIMAL ALGEBRAS
KEIMEL, K
WERNER, H
[J]. MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, (148) : 59 - 85
[9] VARIETIES GENERATED BY PARA PRIMAL ALGEBRAS - (PRELIMINARY-REPORT)
CLARK, DM
KRAUSS, P
[J]. NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1976, 23 (02): : A267 - A267
[10] Algebras defined from ordered sets and the varieties they generate
Berman, J.
Blok, W. J.
[J]. ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2006, 23 (01): : 65 - 88

← 1 2 3 4 5 →