The decision problem for finite algebras from arithmetical varieties with equationally definable principal congruences

1989 ◽  
Vol 26 (1) ◽  
pp. 33-47 ◽  
Author(s):  
Pawe? M. Idziak
Keyword(s):  
Decision Problem ◽  
Finite Algebras ◽  
Equationally Definable Principal Congruences ◽  
Definable Principal Congruences

scholarly journals Varieties generated by finite BCK-algebras

1980 ◽  
Vol 22 (3) ◽  
pp. 411-430 ◽  
Author(s):  
William H. Cornish
Keyword(s):  
Positive Integer ◽  
Finite Algebras ◽  
Equationally Definable Principal Congruences ◽  
Definable Principal Congruences

Iséki's BCK-algebras form a quasivariety of groupoids and a finite BCK-algebra must satisfy the identity (En): xyn = xyn+1, for a suitable positive integer n. The class of BCK-algebras which satisfy (En) is a variety which has strongly equationally definable principal congruences, congruence-3-distributivity, and congruence-3-permutability. Thus, a finite BCK-algebra generates a 3-based variety of BCK-algebras. The variety of bounded commutative BCK-algebras which satisfy (En) is generated by n finite algebras, each of which is semiprimal.

scholarly journals Double MSn-algebras and double Kn.m-algebras

1993 ◽  
Vol 35 (2) ◽  
pp. 189-201 ◽  
Author(s):  
M. Sequeira
Keyword(s):  
Subdirectly Irreducible ◽  
Topological Duality ◽  
Equationally Definable Principal Congruences ◽  
Ockham Algebras ◽  
Definable Principal Congruences ◽  
Subdirectly Irreducible Algebras

AbstractThe variety O2 of all algebras (L; ∧, ∨, f, g, 0, 1) of type (2, 2, 1, 1, 0, 0) such that (L; ∧, ∨, f, 0, 1) and (L; ∧, ∨, g, 0, 1) are Ockham algebras is introduced, and, for n, m εℕ, its subvarieties DMSn, of double MSn-algebras, and DKn,m, of double Kn,m-algebras, are considered. It is shown that DKn,m has equationally definable principal congruences: a description of principal congruences on double Kn,m-algebras is given and simplified for double MSn-algebras. A topological duality for O2-algebras is developed and used to determine the subdirectly irreducible algebras in DKn,m and in DMSn. Finally, MSn-algebras which are reduct of a (unique) double MSn-algebra are characterized.

scholarly journals Fregean subtractive varieties with definable congruence

2001 ◽  
Vol 71 (3) ◽  
pp. 353-366 ◽  
Author(s):  
Paolo Agliano
Keyword(s):  
Hilbert Algebras ◽  
Structure Theorems ◽  
Equationally Definable Principal Congruences ◽  
Subtractive Variety ◽  
Definable Principal Congruences

AbstractIn this paper we investigate subtractive varieties of algebras that are Fregean in order to get structure theorems about them. For instance it turns out that a subtractive variety is Fregean and has equationally definable principal congruences if and only if it is termwise equivalent to a variety of Hilbert algebras with compatible operations. Several examples are provided to illustrate the theory.

Flat algebras and the translation of universal Horn logic to equational logic

2008 ◽  
Vol 73 (1) ◽  
pp. 90-128 ◽  
Author(s):  
Marcel Jackson
Keyword(s):  
Finite Basis ◽  
Equational Logic ◽  
Subdirectly Irreducible ◽  
Horn Logic ◽  
Finite Algebras ◽  
Partial Structures ◽  
Partial Algebras ◽  
Fixed Type ◽  
Bottom Element ◽  
Definable Principal Congruences

AbstractWe describe which subdirectly irreducible flat algebras arise in the variety generated by an arbitrary class of flat algebras with absorbing bottom element. This is used to give an elementary translation of the universal Horn logic of algebras, partial algebras, and more generally still, partial structures into the equational logic of conventional algebras. A number of examples and corollaries follow. For example, the problem of deciding which finite algebras of some fixed type have a finite basis for their quasi-identities is shown to be equivalent to the finite identity basis problem for the finite members of a finiteiy based variety with definable principal congruences.

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