In the paper we prove (Theorem 8.1) that there exists a continuum of non isomorphic simple modules over KF 2 , where F 2 is a free group with 2 generators (compare with [Ca] where a continuum of non isomorphic simple 2-generated groups is constructed). Using this fact we give an example of a non action type logically Noetherian representation (Section 9). In general, the topic of this paper is ...

We define a quasi–projective reduction of a complex algebraic variety X to be a regular map from X to a quasi–projective variety that is universal with respect to regular maps from X to quasi–projective varieties. A toric quasi–projective reduction is the analogous notion in the category of toric varieties. For a given toric variety X we first construct a toric quasi–projective reduction. Then ...

We study automata-theoretic properties of distances and quasi-distances between words. We show that every additive distance is nite. We also show that every additive quasi-distance is regularity-preserving, that is, the neighborhood of any radius of a regular language with respect to an additive quasi-distance is regular. As an application we present a simple algorithm that constructs a metric ...

In the present paper, which is a sequel to [20, 4, 12], we investigate further the structure theory of quasi-MV algebras and √ ′quasi-MV algebras. In particular: we provide a new representation of arbitrary √ ′qMV algebras in terms of √ ′qMV algebras arising out of their MV* term subreducts of regular elements; we investigate in greater detail the structure of the lattice of √ ′qMV varieties, p...

A t-Cayley hypergraph X = t-Cay(G; S) is called normal for a finite group G, if the right regular representationR(G) of G is normal in the full automorphism group Aut(X) of X. In this paper, we investigate the normality of t-Cayley hypergraphs of abelian groups, where S < 4.

Abstract : We call a Cayley graph Γ = Cay (G, S) normal for G, if the right regular representation R(G) of G is normal in the full automorphism group of Aut(Γ). In this paper, a classification of all non-normal Cayley graphs of finite abelian group with valency 6 was presented.