Can there be a structure space-type theory for an arbitrary class of ideals ring? The ideal spaces introduced in this paper allows such study and our includes (but not restricted to) prime, maximal, minimal strongly irreducible, completely proper, minimal, primary, nil, nilpotent, regular, radical, principal, finitely generated ideals. We characterise that are sober. introduce the notion discon...

In this paper we introduce the concept of ideal elements in poe-AG-groupoid and give some characterizations and properties of their ideal elements. So we consider some results concerning ideals in poe-semigroups and investigate them in poe-AG-groupoids. Also, the class of ideal elements of poe-AG-groupoids are studied, certain intrinsic and basic properties of poe-AG-groupoids including: ideal,...

In this paper, with a new idea, we redefine generalized fuzzy ideal and investigate some of its properties. We generalize fuzzy prime ideals and introduce the notions of (∈,∈ ∨q)−fuzzy prime ideal of ordered semigroups. We characterize (∈,∈ ∨q)−fuzzy prime ideal by its image and level ideals. We establish necessary and sufficient condition for fuzzy set to be a (∈,∈ ∨q)−fuzzy prime ideal. 2010 ...

The article deals with the correspondence between soft ideal topological spaces and ones. Investigation of is based on methods general topology, application results for omega open strongly sets given.

All rings in this paper are assumed to be commutative with identity, and they will generally also be Noetherian. In several recent papers the asymptotic theory of ideals in Noetherian rings has been introduced and developed. In this new theory the roles played in the standard theory by associated primes, i?-sequences, classical grade, and Cohen-Macaulay rings are played by, respectively, asympt...

The aim of this paper is to introduce and study set- valued homomorphism on lattices and T-rough lattice with respect to a sublattice. This paper deals with T-rough set approach on the lattice theory. The result of this study contributes to, T-rough fuzzy set and approximation theory and proved in several papers. Keywords: approximation space; lattice; prime ideal; rough ideal; T-rough set; set...

All rings in this paper are commutative and Noetherian. If R is a ring and I ⊂ R is an ideal, cd(R, I) denotes the cohomological dimension of I in R, i.e. the largest integer i such that the i-th local cohomology module H i I(M) doesn’t vanish for some R-module M . For the purposes of this introduction R is a complete equicharacteristic regular local d-dimensional ring with a separably closed r...

The circuit ideal, ICA , of a configuration A = {a1, . . . ,an} ⊂ Z d is the ideal generated by the binomials x + − x − ∈ k[x1, . . . , xn] as c = c − c ∈ Z varies over the circuits of A. This ideal is contained in the toric ideal, IA, of A which has numerous applications and is nontrivial to compute. Since circuits can be computed using linear algebra and the two ideals often coincide, it is w...

In this paper, we study the Hankel edge ideals of graphs. We determine minimal prime ideal labeled Hamiltonian and semi-Hamiltonian graphs, investigate radicality, being a complete intersection, almost intersection set-theoretic for such also consider trees with natural labeling, called rooted labeling. characterize whose is moreover, those initial respect to reverse lexicographic order satisfi...

in this paper we define the notions of ultra and involution ideals in bck-algebras. then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. specially, we show that in a bounded implicative bck-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower bck-semilattice, the notions of...