In this paper, we introduce the notion of fuzzy ideal,fuzzy weak ideal,fuzzy weakly prime left ideal and fuzzy prime left ideal system of a near-subtraction semigroup. We characterize fuzzy weak ideal and fuzzy ideal of a near-subtraction semigroup X through weak ideal and ideal of X respectively. We have shown that a fuzzy left ideal μ of a nearsubtraction semigroup X is a fuzzy weakly prime l...

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...

We consider a commutative ring R graded by an arbitrary abelian group G, and define the grade of a G-homogeneous ideal I on R in terms of vanishing of C̆ech cohomology. By defining the dimension in terms of chains of homogeneous prime ideals and supposing R satisfies a.c.c. on G-homogeneous ideals and has a unique G-homogeneous maximal ideal, we can define graded versions of the depth of R and C...

Let F be a number field with ring of integers OF and D a division F -algebra with a maximal cyclic subfield K. We study rings occurring as quotients of a natural OF -order Λ in D by two-sided ideals. We reduce the problem to studying the ideal structure of Λ/qΛ, where q is a prime ideal in OF , s ≥ 1. We study the case where q remains unramified in K, both when s = 1 and s > 1. This work is mot...

Let (T,M) be a complete local domain containing the integers. Let p1 ⊆ p2 ⊆ · · · ⊆ pn be a chain of nonmaximal prime ideals of T such that Tpn is a regular local ring. We construct a chain of excellent local domains An ⊆ An−1 ⊆ · · · ⊆ A1 such that for each 1 ≤ i ≤ n, the completion of Ai is T , the generic formal fiber of Ai is local with maximal ideal pi, and if I is a nonzero ideal of Ai th...

<p style="text-align: justify;">Let <em>R</em> be a finite commutative ring with identity and <em>P</em> prime ideal of <em>R</em>. The vertex set is <em>R - </em>{0} two distinct vertices are adjacent if their product in <em>P</em>. This graph called the denoted by Γ<sub>P</sub>. relationship among ideal, zero-diviso...

The concept of a closure operator ∇ in an ADL R was introduced. If ∇R is the set of all ∇−invariant elements of R, then the concepts of ∇R−ideal, ∇R−prime ideal are introduced. The interrelations between ∇R−prime ideal and minimal prime ideal of R are derived. If B is the Birkhoff centre of R, then a sufficient condition is derived for a B−ideal to be a minimal prime ideal of R. Mathematics Sub...