Equations implying congruence n-permutability and semidistributivity
نویسنده
چکیده
T. Dent, K. Kearnes and Á. Szendrei have defined the derivative, Σ′, of a set of equations Σ and shown, for idempotent Σ, that Σ implies congruence modularity if Σ′ is inconsistent (Σ′ |= x ≈ y). In this paper we investigate other types of derivatives that give similar results for congruence n-permutability for some n, and for congruence semidistributivity.
منابع مشابه
NOTES ON CONGRUENCE n-PERMUTABILITY AND SEMIDISTRIBUTIVITY
In [1] T. Dent, K. Kearnes and Á. Szendrei define the derivative, Σ′, of a set of equations Σ and show, for idempotent Σ, that Σ implies congruence modularity if Σ′ is inconsistent (Σ′ |= x ≈ y). In this paper we investigate other types of derivatives that give similar results for congruence n-permutable for some n, and for congruence semidistributivity. In a recent paper [1] T. Dent, K. Kearne...
متن کاملCongruence join semidistributivity is equivalent to a congruence identity
We show that a locally finite variety is congruence join semidistributive if and only if it satisfies a congruence identity that is strong enough to force join semidistributivity in any lattice.
متن کاملWeak Congruence Semidistributivity Laws and Their Conjugates
Lattice Horn sentences including Geyer’s SD(n, 2) and their conjugates C(n, 2) are considered. SD(2, 2) is the meet semidistributivity law SD∧. Both SD(n, 2) and C(n, 2) become strictly weaker when n grows. For varieties V the satisfaction of SD(n, 2) in {Con(A) : A ∈ V} is characterized by a Mal’cev condition. Using this Mal’cev condition it is shown that C(n, 2) |=con SD(n, 2), which means th...
متن کاملA Scheme for Congruence Semidistributivity
A diagrammatic statement is developed for the generalized semidistributive law in case of single algebras assuming that their congruences are permutable. Without permutable congruences, a diagrammatic statement is developed for the ∧-semidistributive law.
متن کاملA Finite Basis Theorem for Residually Finite, Congruence Meet-Semidistributive Varieties
We derive a Mal'cev condition for congruence meet-semidistributivity and then use it to prove two theorems. Theorem A: if a variety in a nite language is congruence meet-semidistributive and residually less than some nite cardinal, then it is nitely based. Theorem B: there is an algorithm which, given m < ! and a nite algebra in a nite language, determines whether the variety generated by the a...
متن کامل