The identities of ? and unique subdirect factorization within ? classes of universal algebras

1955 ◽  
Vol 62 (1) ◽  
pp. 171-188 ◽  
Author(s):  
Alfred L. Foster
Keyword(s):  
Universal Algebras ◽  
Subdirect Factorization

scholarly journals Independence of algebras with edge term

2015 ◽  
Vol 25 (07) ◽  
pp. 1145-1157 ◽  
Author(s):  
Erhard Aichinger ◽  
Peter Mayr
Keyword(s):  
Polynomial Time ◽  
Sufficient Conditions ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Universal Algebras ◽  
Finite Algebras ◽  
Necessary And Sufficient ◽  
Independent Varieties ◽  
Subdirect Factorization ◽  
Independence Of Algebras

In [A. L. Foster, The identities of — and unique subdirect factorization within — classes of universal algebras, Math. Z. 62 (1955) 171–188], two varieties [Formula: see text] of the same type are defined to be independent if there is a binary term [Formula: see text] such that [Formula: see text] and [Formula: see text]. In this paper, we give necessary and sufficient conditions for two finite algebras with a Mal’cev term (or, more generally, with an edge term) to generate independent varieties. In particular we show that the independence of finitely generated varieties with edge term can be decided by a polynomial time algorithm.

Weak Products of Simple Universal Algebras

1969 ◽  
Vol 42 (1-3) ◽  
pp. 157-171 ◽  
Author(s):  
Tah-Kai Hu
Keyword(s):  
Universal Algebras

WHITEHEAD EXACT SEQUENCE AND DIFFERENTIAL GRADED FREE LIE ALGEBRA

2004 ◽  
Vol 15 (10) ◽  
pp. 987-1005 ◽  
Author(s):  
MAHMOUD BENKHALIFA
Keyword(s):  
Exact Sequence ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Integral Domain ◽  
Free Lie Algebra ◽  
Universal Algebras ◽  
Free Lie Algebras ◽  
Equivalent Class

Let R be a principal and integral domain. We say that two differential graded free Lie algebras over R (free dgl for short) are weakly equivalent if and only if the homologies of their corresponding enveloping universal algebras are isomophic. This paper is devoted to the problem of how we can characterize the weakly equivalent class of a free dgl. Our tool to address this question is the Whitehead exact sequence. We show, under a certain condition, that two R-free dgls are weakly equivalent if and only if their Whitehead sequences are isomorphic.

Varieties of infinitary universal algebras

1985 ◽  
Vol 20 (1) ◽  
pp. 123-126
Author(s):  
Ji?� Rosick�
Keyword(s):  
Universal Algebras

scholarly journals Universal algebras with all operations of bounded range

1974 ◽  
Vol 30 (2) ◽  
pp. 177-185 ◽  
Author(s):  
I. G. Rosenberg
Keyword(s):  
Universal Algebras

Finiteness of Semigroups of Operators in Universal Algebra

1967 ◽  
Vol 19 ◽  
pp. 764-768 ◽  
Author(s):  
Evelyn Nelson
Keyword(s):  
Universal Algebra ◽  
Partial Solution ◽  
Semigroups Of Operators ◽  
Ordered Semigroups ◽  
Universal Algebras ◽  
Partially Ordered ◽  
Master's Thesis ◽  
Mcmaster University

This paper is a partial solution of problem 24 in (2) which suggests that the finiteness of the partially ordered semigroups generated by various combinations of operators on classes of universal algebras be investigated. The main result is that the semigroups generated by the following sets of operators (for definitions see §2) are finite: {H, S, P, Ps}, {C, H, S, P, PF} {C, H, S, PU, PF}.This paper is part of the author's Master's thesis written in the Department of Mathematics at McMaster University. The author is indebted to the referee for his helpful suggestions.

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