On function algebras in which every congruence is determined by a filter

AbstractWe prove that the congruences of a function algebra which belongs to a sufficiently strong type have a nice structure. Every congruence is determined by the filter which supports it. As a consequence we are able to clarify the structure of left ideals in the near-ring of all functions from a group (G, +) into itself. Also, we investigate function algebras where every invariant subalgebra is determined by its image

Embedding coproducts of partition lattices

We prove that the lattice Eq(X) of all equivalence relations on an infinite set X contains, as a 0,1-sublattice, the 0-coproduct of two copies of itself, thus answering a question by G.M. Bergman. Hence, by using methods initiated by de Bruijn and further developed by Bergman, we obtain that Eq(X) also contains, as a sublattice, the coproduct of 2^{card(X)} copies of itself.Comment: To appear in Acta Sci. Math. (Szeged

(T, S) vague congruence and . . .

The aim of this paper is to further develop the concept of (T, S) vague equivalence relation. We discuss some characterization of vague equivalence and vague congruence relations in terms of their level set and prove that the class of vague congruence relations forms a distributive lattice. Further, we define the quotient of a vague lattice with respect to a congruence relation