The minimal prime decomposition for semiprime ideals is defined and studied on z-ideals of C(X). The necessary and sufficient condition for existence of the minimal prime decomposition of a z-ideal / is given, when / satisfies one of the following conditions: (i) / is an intersection of maximal ideals. (ii) I is an intersection of O , s, when X is basically disconnected. (iii) I=O , when x X h...

in this paper, the notion of maximal m-open set is introduced and itsproperties are investigated. some results about existence of maximal m-open setsare given. moreover, the relations between maximal m-open sets in an m-spaceand maximal open sets in the corresponding generated topology are considered.our results are supported by examples and counterexamples.

We describe applications of Koszul cohomology to the BrillNoether theory of rank 2 vector bundles. Among other things, we show that in every genus g > 10, there exist curves invalidating Mercat’s Conjecture for rank 2 bundles. On the other hand, we prove that Mercat’s Conjecture holds for general curves of bounded genus, and its failure locus is a Koszul divisor in the moduli space of curves. W...

Several Krylov-type procedures are introduced that generalize matrix Krylov methods for tensor computations. They are denoted minimal Krylov recursion, maximal Krylov recursion, and contracted tensor product Krylov recursion. It is proved that, for a given tensor A with multilinear rank-(p, q, r), the minimal Krylov recursion extracts the correct subspaces associated to the tensor in p+ q+r num...

In this paper we classify fuzzy subgroups of a rank-3 abelian group $G = mathbb{Z}_{p^n} + mathbb{Z}_p + mathbb{Z}_p$ for any fixed prime $p$ and any positive integer $n$, using a natural equivalence relation given in cite{mur:01}. We present and prove explicit polynomial formulae for the number of (i) subgroups, (ii) maximal chains of subgroups, (iii) distinct fuzzy subgroups, (iv) non-isomorp...

Abstract. The poset of noncrossing partitions can be naturally defined for any finite Coxeter group W . It is a self-dual, graded lattice which reduces to the classical lattice of noncrossing partitions of {1, 2, . . . , n} defined by Kreweras in 1972 when W is the symmetric group Sn, and to its type B analogue defined by the second author in 1997 when W is the hyperoctahedral group. We give a ...

The triple factorization of a group $G$ has been studied recently showing that $G=ABA$ for some proper subgroups $A$ and $B$ of $G$, the definition of rank-two geometry and rank-two coset geometry which is closely related to the triple factorization was defined and calculated for abelian groups. In this paper we study two infinite classes of non-abelian finite groups $D_{2n}$ and $PSL(2,2^{n})$...