Varieties of Lattices

2016 ◽  
pp. 1-26
Author(s):  
P. Jipsen ◽  
H. Rose
Keyword(s):  
Varieties Of Lattices

Term rewrite systems and varieties of lattices

1995 ◽  
pp. 255-277
Author(s):  
Ralph Freese ◽  
Jaroslav Jezek ◽  
J. Nation
Keyword(s):  
Rewrite Systems ◽  
Varieties Of Lattices ◽  
Term Rewrite Systems

scholarly journals VARIETIES WHOSE TOLERANCES ARE HOMOMORPHIC IMAGES OF THEIR CONGRUENCES

2012 ◽  
Vol 87 (2) ◽  
pp. 326-338 ◽  
Author(s):  
GÁBOR CZÉDLI ◽  
EMIL W. KISS
Keyword(s):  
Homomorphic Image ◽  
Tolerance Relation ◽  
Varieties Of Lattices ◽  
Majority Term

AbstractThe homomorphic image of a congruence is always a tolerance (relation) but, within a given variety, a tolerance is not necessarily obtained this way. By a Maltsev-like condition, we characterise varieties whose tolerances are homomorphic images of their congruences (TImC). As corollaries, we prove that the variety of semilattices, all varieties of lattices, and all varieties of unary algebras have TImC. We show that a congruence n-permutable variety has TImC if and only if it is congruence permutable, and construct an idempotent variety with a majority term that fails TImC.

Cut elimination and word problems for varieties of lattices

1981 ◽  
Vol 12 (1) ◽  
pp. 290-321 ◽  
Author(s):  
Jürgen Schulte Mönting
Keyword(s):  
Word Problems ◽  
Cut Elimination ◽  
Varieties Of Lattices

A Remark on Varieties of Lattices and Semigroups

1969 ◽  
Vol 21 (2) ◽  
pp. 394 ◽  
Author(s):  
Richard A. Dean ◽  
Trevor Evans
Keyword(s):  
Varieties Of Lattices

Mapping Extension of an Algebra

2009 ◽  
Vol 16 (03) ◽  
pp. 479-494
Author(s):  
Adam W. Marczak ◽  
Jerzy Płonka
Keyword(s):  
Boolean Algebras ◽  
Equational Class ◽  
Combinatorial Properties ◽  
Varieties Of Lattices ◽  
Nullary Operation ◽  
New Construction ◽  
Fixed Type

A new construction of algebras called a mapping extension of an algebra is here introduced. The construction yields a generalization of some classical constructions such as the nilpotent extension of an algebra, inflation of a semigroup but also the square extension construction introduced recently for idempotent groupoids. The mapping extension construction is defined for algebras of any fixed type, however nullary operation symbols are here not admitted. It is based on the notion of a retraction and some system of mappings. A mapping extension of a given algebra is constructed as a counterimage algebra by a specially defined retraction. Varieties of algebras satisfying an identity φ(x) ≈ x for a term φ not being a variable (such as varieties of lattices, Boolean algebras, groups and rings) are especially interesting because for such a variety [Formula: see text], all mapping extensions by φ of algebras from [Formula: see text] form an equational class. In the last section, combinatorial properties of the mapping extension construction are considered.

scholarly journals Frattini sublattices in varieties of lattices

1981 ◽  
Vol 44 (2) ◽  
pp. 181-184 ◽  
Author(s):  
M. E. Adams ◽  
J. Sichler
Keyword(s):  
Varieties Of Lattices

Intersection of noncharacterizable varieties of lattices

1990 ◽  
Vol 29 (3) ◽  
pp. 224-228 ◽  
Author(s):  
Zh. A. Omarov
Keyword(s):  
Varieties Of Lattices

Varieties of Lattices

2003 ◽  
pp. 295-342 ◽  
Author(s):  
George Grätzer
Keyword(s):  
Varieties Of Lattices
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