Equational classes of relative Stone algebras.

Equational and implicational classes of co-algebras

If F : Set → Set is a functor which is bounded and preserves weak generalized pullbacks then a class of F-coalgebras is a covariety, i.e., closed under H (homomorphic images), S (sub-coalgebras) and ∑ (sums), if and only if it can be de0ned by a set of “coequations”. Similarly, quasi-covarieties, i.e., classes closed under H and ∑ , can be characterized by implications of coequations. These res...

Dualities for Equational Classes of Brouwerian Algebras and Heyting Algebras

This paper focuses on the equational class S„ of Brouwerian algebras and the equational class L„ of Heyting algebras generated by an »-element chain. Firstly, duality theories are developed for these classes. Next, the projectives in the dual categories are determined, and then, by applying the dualities, the injectives and absolute subretracts in Sn and L„ are characterized. Finally, free prod...

Spectral algebras for strong equational classes of partial algebras

As it is well known, the generalization of universal-algebraic notions to partial algebras yields different kinds of homomorphisms, subalgebras, validity of equations etc. Three types of equations: existential, weak and strong, have been investigated by many algebraists with interesting results on algebraic characterization of equationally definable classes of partial algebras. One of the most ...

FUZZY EQUATIONAL CLASSES ARE FUZZY VARIETIES

In the framework of fuzzy algebras with fuzzy equalities and acomplete lattice as a structure of membership values, we investigate fuzzyequational classes. They consist of special fuzzy algebras fullling the samefuzzy identities, dened with respect to fuzzy equalities. We introduce basicnotions and the corresponding operators of universal algebra: construction offuzzy subalgebras, homomorphisms...

Equational Logic and Equational Theories of Algebras