Small congruence distributive varieties: Retracts, injectives, equational compactness and amalgamation

1996 ◽  
Vol 33 (3) ◽  
pp. 207-228 ◽  
Author(s):  
P. Ouwehand ◽  
H. Rose
Keyword(s):  
Small Congruence ◽  
Equational Compactness ◽  
Congruence Distributive

Algebraically closed algebras in certain small congruence distributive varieties

2009 ◽  
Vol 61 (2) ◽  
pp. 247-260 ◽  
Author(s):  
P. Ouwehand
Keyword(s):  
Small Congruence ◽  
Congruence Distributive

scholarly journals CONGRUENCE FD-MAXIMAL VARIETIES OF ALGEBRAS

2012 ◽  
Vol 22 (06) ◽  
pp. 1250053 ◽  
Author(s):  
PIERRE GILLIBERT ◽  
MIROSLAV PLOŠČICA
Keyword(s):  
Necessary Condition ◽  
Finitely Generated ◽  
Distributive Variety ◽  
Finite Lattices ◽  
Congruence Lattices ◽  
Congruence Distributive Variety ◽  
Congruence Distributive ◽  
Special Congruence

We study the class of finite lattices that are isomorphic to the congruence lattices of algebras from a given finitely generated congruence-distributive variety. If this class is as large as allowed by an obvious necessary condition, the variety is called congruence FD-maximal. The main results of this paper characterize some special congruence FD-maximal varieties.

Subdirect irreducibility and equational compactness in unary algebras

1970 ◽  
Vol 21 (1) ◽  
pp. 256-264 ◽  
Author(s):  
G�nter H. Wenzel
Keyword(s):  
Subdirect Irreducibility ◽  
Equational Compactness

scholarly journals Equational compactness in infinitary algebras

1973 ◽  
Vol 27 (2) ◽  
pp. 197-205 ◽  
Author(s):  
Bernhard Banaschewski ◽  
Evelyn Nelson
Keyword(s):  
Equational Compactness

scholarly journals Another characterization of congruence distributive varieties

2020 ◽  
Vol 57 (3) ◽  
pp. 284-289
Author(s):  
Paolo Lipparini
Keyword(s):  
Natural Number ◽  
Congruence Identity ◽  
Congruence Distributive

AbstractWe provide a Maltsev characterization of congruence distributive varieties by showing that a variety 𝓥 is congruence distributive if and only if the congruence identity … (k factors) holds in 𝓥, for some natural number k.

scholarly journals CRITICAL POINTS OF PAIRS OF VARIETIES OF ALGEBRAS

2009 ◽  
Vol 19 (01) ◽  
pp. 1-40 ◽  
Author(s):  
PIERRE GILLIBERT
Keyword(s):  
Natural Number ◽  
Critical Points ◽  
Modular Lattice ◽  
General Theorem ◽  
Finitely Generated ◽  
Congruence Distributive

For a class [Formula: see text] of algebras, denote by Conc[Formula: see text] the class of all (∨, 0)-semilattices isomorphic to the semilattice ConcA of all compact congruences of A, for some A in [Formula: see text]. For classes [Formula: see text] and [Formula: see text] of algebras, we denote by [Formula: see text] the smallest cardinality of a (∨, 0)-semilattices in Conc[Formula: see text] which is not in Conc[Formula: see text] if it exists, ∞ otherwise. We prove a general theorem, with categorical flavor, that implies that for all finitely generated congruence-distributive varieties [Formula: see text] and [Formula: see text], [Formula: see text] is either finite, or ℵn for some natural number n, or ∞. We also find two finitely generated modular lattice varieties [Formula: see text] and [Formula: see text] such that [Formula: see text], thus answering a question by J. Tůma and F. Wehrung.

scholarly journals Uniform Mal’cev algebras with small congruence lattices

2014 ◽  
Vol 72 (1) ◽  
pp. 57-69
Author(s):  
Nebojša Mudrinski
Keyword(s):  
Congruence Lattices ◽  
Mal’Cev Algebras ◽  
Small Congruence

Congruence—distributive polynomial reducts of lattices

1979 ◽  
Vol 9 (1) ◽  
pp. 142-145 ◽  
Author(s):  
Kirby A. Baker
Keyword(s):  
Congruence Distributive

The determination of subvarieties of certain congruence-distributive varieties

1994 ◽  
Vol 32 (1) ◽  
pp. 44-62 ◽  
Author(s):  
H. A. Priestley
Keyword(s):  
Congruence Distributive

Salary comparison: Internal and External (In)Congruence, Distributive Justice, and Employee Withdrawal

2020 ◽  
Vol 2020 (1) ◽  
pp. 21604
Author(s):  
Xiaomin Xu ◽  
Ishbel McWha-Hermann
Keyword(s):  
Distributive Justice ◽  
Employee Withdrawal ◽  
Congruence Distributive
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