Congruence join semidistributivity is equivalent to a congruence identity
نویسنده
چکیده
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.
منابع مشابه
Equations implying congruence n-permutability and semidistributivity
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.
متن کاملMyhill-Nerode Fuzzy Congruences Corresponding to a General Fuzzy Automata
Myhill-Nerode Theorem is regarded as a basic theorem in the theories of languages and automata and is used to prove the equivalence between automata and their languages. The significance of this theorem has stimulated researchers to develop that on different automata thus leading to optimizing computational models. In this article, we aim at developing the concept of congruence in general fuzzy...
متن کاملThe Lattice of Lambda Theories ( Regular Research Paper )
The lattice Ì of lambda theories is isomorphic to the congruence lattice of the term algebra of the minimal lambda theory ¬. This remark is the starting point for studying the structure of Ì by universal algebraic methods. In this paper we show that Ì satisfies nontrivial lattice quasi-identities, while we conjecture that Ì does not satisfy any nontrivial lattice identity (a lattice identity is...
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 کاملNOTES 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 کامل