Let $R$ be an associative ring and let $M$ be a left $R$-module.Let $Spec_{R}(M)$ be the collection of all prime submodules of $M$ (equipped with classical Zariski topology). There is a conjecture which says that every irreducible closed subset of $Spec_{R}(M)$ has a generic point. In this article we give an affirmative answer to this conjecture and show that if $M$ has a Noetherian spectrum, t...

Abstract We prove a hom-associative version of Hilbert’s basis theorem, which includes as special cases both non-associative and the classical theorem for associative Ore extensions. Along way, we develop hom-module theory. conclude with some examples extensions are all noetherian by our theorem.

In this paper, we discuss various k-g inverses associated with a k-regular Interval-Valued Fuzzy Matrix. We obtain some characterization of the set of all k-g inverses.

This is the announcement, and the long summary, of a series of articles on the algorithmic study of Thurston maps. We describe branched coverings of the sphere in terms of group-theoretical objects called bisets, and develop a theory of decompositions of bisets. We introduce a canonical “Levy” decomposition of an arbitrary Thurston map into homeomorphisms, metrically-expanding maps and maps dou...

An integral component of Fuzzy ARTMAP's training phase is the use of Match Tracking (MT), whose functionality is to search for an appropriate category that will correctly classify a presented training pattern in case this particular pattern was originally misclassified. In this paper we explain the MT's role in detail, why it actually works and finally we put its usefulness to the test by compa...