In this paper we describe three different variations of prime ideals: strongly irreducible ideals, ideals and insulated in the context Leavitt path algebras. We give necessary sufficient conditions under which a proper ideal algebra L is product as well an intersection finitely many these types ideals. Such factorizations, when they are irredundant, shown to be unique except for order factors. ...

We define a class of L-convex-concave subsets of RP n , where L is a projective sub-space of dimension l in RP n. These are sets whose sections by any (l+1)-dimensional space L ′ containing L are convex and concavely depend on L ′. We introduce an L-duality for these sets, and prove that the L-dual to an L-convex-concave set is an L *-convex-concave subset of (RP n) *. We discuss a version of A...

The space of unitary local systems of rank one on the complement of an arbitrary divisor in a complex projective algebraic variety can be described in terms of parabolic line bundles. This space is a natural setting for studying global invariants of singularities involving multiplier ideals. We show that multiplier ideals provide natural stratifications of this space. We prove a structure theor...

In this paper, L-convex ?*-remotehood system is introduced and some characterizations of both L-convexity remotehood are obtained. Further, ?*-remote mapping presented its properties investigated. Based on this, quasi-uniformity quasiuniformity preserving introduced. It proved that quasi-uniform space Lconvex mutually induced. addition, the category spaces can be embedded into spaces.

The goal of this paper is to introduce the notions of , -double fuzzy ideals and , -double fuzzy ideal bases where and are strictly two-sided, commutative quanta and also investigate the relationships between these two structures. Then, we construct a functor from the category of , -double fuzzy ideal spaces to the category of , -double fuzzy cotopological spaces. Furthermore, we show the exist...

The goal of local class field theory is to classify abelian Galois extensions of a local field K. Several definitions of local fields are in use. In this thesis, local fields, which will be defined explicitly in Section 2, are fields that are complete with respect to a discrete valuation and have a finite residue field. A prototypical first example is Qp, the completion of Q with respect to the...

An rj-normal lattice is a distributive lattice with 0 such that each prime ideal contains at most n minimal prime ideals. A relatively ra-normal lattice is a distributive lattice such that each bounded closed interval is an /¡.-normal lattice. The main results of this paper are: (1) a distributive lattice L with 0 is 71,-normal if and only if for any %n, x,,*•', X e L such that x Ax. = 0 for an...