T. Katri n ak proved the following theorem: Every nite distributive lattice is the congruence lattice of a nite p-algebra. We provide a short proof, and a generalization, of this result.

First, we introduce the concept of intuitionistic fuzzy group congruenceand we obtain the characterizations of intuitionistic fuzzy group congruenceson an inverse semigroup and a T^{*}-pure semigroup, respectively. Also,we study some properties of intuitionistic fuzzy group congruence. Next, weintroduce the notion of intuitionistic fuzzy semilattice congruence and we givethe characterization of...

This paper deals with a new analytic type of vectorand Clifford algebra valued automorphic forms in one and two vector variables. For hypercomplex generalizations of the classical modular group and their arithmetic congruence subgroups Eisensteinand Poincaré type series that are annihilated by Dirac operators, and more generally, by iterated Dirac operators on the upper half-space of Rn are dis...

A finite lattice is representable if it is isomorphic to the congruence lattice of a finite algebra. In this paper, we develop methods by which we can construct new representable lattices from known ones. The techniques we employ are sufficient to show that every finite lattice which contains no three element antichains is representable. We then show that if an order polynomially complete latti...

We introduce a new class of lattices, the modernistic lattices, and their duals, the comodernistic lattices. We show that every modernistic or comodernistic lattice has shellable order complex. We go on to exhibit a large number of examples of (co)modernistic lattices. We show comodernism for two main families of lattices that were not previously known to be shellable: the order congruence latt...

In this paper we introduce the concept of an (L; ')-representation of an algebra A which is a common generalization of subdirect, full subdirect and weak direct representation of A. Here we characterize such representations in terms of congruence relations.