Multiplier ideals in commutative rings are certain integrally closed ideals with properties that lend themselves to highly interesting applications. How special are they among integrally closed ideals in general? We show that in a two-dimensional regular local ring with algebraically closed residue field there is in fact no difference between “multiplier” and “integrally closed” (or “complete.”...

In this paper authors have given a separation theorem for α ideals in a 0distributive lattice. Some characterizations of semi prime ideals have been discussed. Then they have included an interesting result on *-ideals in a p-algebra by using the properties of semi prime ideals.

We introduce the notion of a generalized semi-ideal in a ternary semiring. Various examples to establish a relationship between ideals, bi-ideals, quasi-ideals and generalized semi-ideals are furnished. A criterion for a commutative ternary semiring without any divisors of zero to a ternary division semiring is given. AMS Mathematics Subject Classification (2010): 16Y60, 16Y99

In this paper, we consider the intuitionistic fuzzification of the concept of p-ideals in BCI-algebras and investigate some of their properties. Intuitionistic fuzzy p-ideals are connected with intuitionistic fuzzy ideals and intuitionistic fuzzy subalgebras. Moreover, intuitionistic fuzzy p-ideals are characterized using level subsets, homomorphic pre-images, and intuitionistic fuzzy ideal ext...

We introduce the notion of Smarandache BCH-algebra and Smarandache (fresh, clean and fantastic) ideals, some example are given and related properties are investigated. Relationship between Q-Smarandache (fresh, clean and fantastic) ideals and other types of ideals are given. Extension properties for Q-Smarandache (fresh, clean and fantastic) ideals are established.

In this paper, we first introduce the new concept of completely semiprime fuzzy ideals of an ordered semigroup S, which is an extension of completely semiprime ideals of ordered semigroup S, and investigate some its related properties. Especially, we characterize an ordered semigroup that is a semilattice of simple ordered semigroups in terms of completely semiprime fuzzy ideals of ordered semi...

Quasi-stable ideals appear as leading ideals in the theory of Pommaret bases. We show that quasi-stable leading ideals share many of the properties of the generic initial ideal. In contrast to genericity, quasistability is a characteristic independent property that can be effectively verified. We also relate Pommaret bases to some invariants associated with local cohomology, exhibit the existen...

In this paper, the concept of interval-valued intuitionistic fuzzy set to UP subalgebras and UP -ideals of UP -algebras are introduced. Relations among IVIF UP subalgebras with IVIF UP -ideals of UP -algebras are investigated. The homomorphic image and inverse image of IVIF UP -subalgebras and IVIF UP -ideals are studied and some related properties are investigated. Equivalence relations on IVI...

A weaker form of the multiplicity conjecture of Herzog, Huneke, and Srinivasan is proven for two classes of monomial ideals: quadratic monomial ideals and squarefree monomial ideals with sufficiently many variables relative to the Krull dimension. It is also shown that tensor products, as well as Stanley-Reisner ideals of certain unions, satisfy the multiplicity conjecture if all the components...

Demailly, Ein and Lazarsfeld [DEL] proved the subadditivity theorem for multiplier ideals, which states the multiplier ideal of the product of ideals is contained in the product of the individual multiplier ideals, on non-singular varieties. We prove that, in two-dimensional case, the subadditivity theorem holds on log-terminal singularities. However, in higher dimensional case, we have several...