On schemes for congruence distributivity

2004 ◽  
Vol 2 (3) ◽  
pp. 368-376
Author(s):  
I. Chajda ◽  
R. Halaš
Keyword(s):  
Congruence Distributivity

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.

scholarly journals Facets of congruence distributivity in Goursat categories

2020 ◽  
Vol 224 (10) ◽  
pp. 106380
Author(s):  
Marino Gran ◽  
Diana Rodelo ◽  
Idriss Tchoffo Nguefeu
Keyword(s):  
Congruence Distributivity

scholarly journals The Tschantz and the alvin higher conditions are equivalent in congruence distributive varieties

2020 ◽  
Vol 82 (1) ◽  
Author(s):  
Paolo Lipparini
Keyword(s):  
Strong Sense ◽  
Congruence Distributivity ◽  
Congruence Modularity ◽  
Congruence Distributive

AbstractWe show that, under the assumption of congruence distributivity, a condition by S. Tschantz characterizing congruence modularity is equivalent to a variant of the classical Jónsson condition. Here equivalence is intended in a strong sense, to the effect that the corresponding sequences of terms have exactly the same length.

Few subpowers, congruence distributivity and near-unanimity terms

2008 ◽  
Vol 58 (2) ◽  
pp. 119-128 ◽  
Author(s):  
Petar Marković ◽  
Ralph McKenzie
Keyword(s):  
Congruence Distributivity ◽  
Near Unanimity

scholarly journals Trees as commutative BCK-Algebras

1981 ◽  
Vol 23 (2) ◽  
pp. 181-190
Author(s):  
William H. Cornish
Keyword(s):  
Height Function ◽  
Chain Condition ◽  
New Method ◽  
Subdirectly Irreducible ◽  
Natural Numbers ◽  
Finitely Generated ◽  
Congruence Distributivity ◽  
Finite Height ◽  
Descending Chain Condition ◽  
Simple Algebras

A new method of constructing commutative BCK-algebras is given. It depends upon the notion of a valuation of a lower semilattice in a given commutative BCK-algebra. Any tree vith the descending chain condition has a valuation in the natural numbers, considered as a commutative BCK-algebra; the valuation is the height-function. Thus, any tree of finite height possesses a uniquely determined commutative BCK-structure. The finite trees with at most one atom and height at most n are precisely the finitely generated subdirectly irreducible (simple) algebras in the subvariety of commutative BCK-algebras which satisfy the identity (En): xyn = xyn+1. Due to congruence-distributivity, it is then possible to describe the associated lattice of subvarieties.

scholarly journals ON THE COMPLEXITY OF SOME MALTSEV CONDITIONS

2009 ◽  
Vol 19 (01) ◽  
pp. 41-77 ◽  
Author(s):  
RALPH FREESE ◽  
MATTHEW A. VALERIOTE
Keyword(s):  
Polynomial Time ◽  
Finite Algebra ◽  
Free Algebras ◽  
Congruence Distributivity ◽  
Sharp Bounds ◽  
Polynomial Time Algorithms ◽  
Maltsev Conditions

This paper studies the complexity of determining if a finite algebra generates a variety that satisfies various Maltsev conditions, such as congruence distributivity or modularity. For idempotent algebras we show that there are polynomial time algorithms to test for these conditions but that in general these problems are EXPTIME complete. In addition, we provide sharp bounds in terms of the size of two-generated free algebras on the number of terms needed to witness various Maltsev conditions, such as congruence distributivity.

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