Congruence modularity implies the Arguesian identity

1976 ◽  
Vol 6 (1) ◽  
pp. 225-228 ◽  
Author(s):  
Ralph Freese ◽  
Bjarni Jónsson
Keyword(s):  
Congruence Modularity

Congruence modularity at 0

2011 ◽  
Vol 66 (1-2) ◽  
pp. 63-67
Author(s):  
Benedek Skublics
Keyword(s):  
Congruence Modularity

3–3 lattice inclusions imply congruence modularity

1977 ◽  
Vol 7 (1) ◽  
pp. 191-194 ◽  
Author(s):  
Ralph Freese ◽  
J. B. Nation
Keyword(s):  
Congruence Modularity

scholarly journals Monotone clones, residual smallness and congruence distributivity

1990 ◽  
Vol 41 (2) ◽  
pp. 283-300 ◽  
Author(s):  
Ralph McKenzie
Keyword(s):  
Ordered Set ◽  
Ordered Sets ◽  
Congruence Distributivity ◽  
Congruence Modularity ◽  
Congruence Distributive

Corresponding to each ordered set there is a variety, determined up to equivalence, generated by an algebra whose term operations are all the monotone operations on the ordered set. We produce several characterisations of the finite bounded ordered sets for which the corresponding variety is congruence-distributive. In particular, we find that congruence-distributivity, congruence-modularity, and residual smallness are equivalent for these varieties.

A Characterization of Identities Implying Congruence Modularity I

1980 ◽  
Vol 32 (5) ◽  
pp. 1140-1167 ◽  
Author(s):  
Alan Day ◽  
Ralph Freese
Keyword(s):  
Variety Of Algebras ◽  
Congruence Modularity ◽  
Lattice Identity ◽  
Congruence Lattices

In his thesis and [24], J. B. Nation showed the existence of certain lattice identities, strictly weaker than the modular law, such that if all the congruence lattices of a variety of algebras satisfy one of these identities, then all the congruence lattices were even modular. Moreover Freese and Jónsson showed in [10] that from this “congruence modularity” of a variety of algebras one can even deduce the (stronger) Arguesian identity.These and similar results [3; 5; 9; 12; 18; 21] induced Jónsson in [17; 18] to introduce the following notions. For a variety of algebras , is the (congruence) variety of lattices generated by the class () of all congruence lattices θ(A), . Secondly if is a lattice identity, and Σ is a set of such, holds if for any variety implies .

Lattice conditions implying congruence modularity

1976 ◽  
Vol 6 (1) ◽  
pp. 291-301 ◽  
Author(s):  
Alan Day
Keyword(s):  
Congruence Modularity

On the congruence modularity conjecture

2006 ◽  
Vol 55 (4) ◽  
pp. 495-508 ◽  
Author(s):  
Luís Sequeira
Keyword(s):  
Congruence Modularity
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