Quasi-socle ideals and Goto numbers of parameters

Quasi-socle Ideals and Goto Numbers of Parameters

Goto numbers g(Q) = max{q ∈ Z | Q : m is integral overQ} for certain parameter ideals Q in a Noetherian local ring (A,m) with Gorenstein associated graded ring G(m) = ⊕ n≥0 m /m are explored. As an application, the structure of quasisocle ideals I = Q : m (q ≥ 1) in a one-dimensional local complete intersection and the question of when the graded rings G(I) = ⊕ n≥0 I /I are Cohen-Macaulay are s...

The Goto Numbers of Parameter Ideals

Let Q be a parameter ideal of a Noetherian local ring (R, m). The Goto number g(Q) of Q is the largest integer g such that Q : m is integral over Q. We examine the values of g(Q) as Q varies over the parameter ideals of R. We concentrate mainly on the case where dimR = 1, and many of our results concern parameter ideals of a numerical semigroup ring.

Algebraic and topological aspects of quasi-prime ideals

In this paper, we define the new notion of quasi-prime ideal which generalizes at once both prime ideal and primary ideal notions. Then a natural topology on the set of quasi-prime ideals of a ring is introduced which admits the Zariski topology as a subspace topology. The basic properties of the quasi-prime spectrum are studied and several interesting results are obtained. Specially, it is pro...

Interval-valued fuzzy quasi-ideals and bi-ideals of semirings

Abstract. The interval-valued prime fuzzy ideals (in brevity, the iv. prime fuzzy ideals) of a semigroup have been recently studied by Kar, Sarkar and Shum [18]. As a continued study of i-v fuzzy ideals, we are going to investigate the properties of i-v fuzzy quasi-ideal and i-v fuzzy bi-ideal of a semiring and then we characterize the regularity and intra-regularity of a semiring in terms of t...

(λ, μ)-Fuzzy Version of Ideals, Interior Ideals, Quasi-Ideals, and Bi-Ideals