A characterization of an h-hemiregular hemiring in terms of a fuzzy h-ideal is provided. Some properties of prime fuzzy h-ideals of h-hemiregular hemirings are investigated. It is proved that a fuzzy subset f of a hemiring S is a prime fuzzy left (right) h-ideal of S if and only if f is two-valued, f(0) = 1, and the set of all x in S such that f(x) = 1 is a prime (left) right h-ideal of S. Fina...

The concept of  -ideals is introduced in an Almost Distributive lattice(ADL) with respect to a congruence and the properties of  -ideals are studied. Derived a set of equivalent conditions for a  -ideal to become a  -prime ideal.

the notion of vague ideals in pseudo mv-algebras is introduced,and several properties are investigated. conditions for a vague set to be avague ideal are provided. conditions for a vague ideal to be implicative aregiven. characterizations of (implicative, prime) vague ideals are discussed.the smallest vague ideal containing a given vague set is established. primeand implicative extension proper...

For a ring endomorphism α and an α-derivation δ, we introduce α-compatible ideals which are a generalization of α-rigid ideals and study the connections of the prime radical and the upper nil radical of R with the prime radical and the upper nil radical of the Ore extension R[x;α, δ] and the skew power series R[[x;α]]. As a consequence we obtain a generalization of Hong, Kwak and Rizvi, 2005.

We provide methods to do explicit calculations in a polynomial ring in finitely many variables over a field. We develop algorithms to compute quotients of ideals, the radical of an ideal and a primary decomposition of an ideal. We also present methods to solve explicit tasks such as testing for prime ideals or identical ideals.

Using a generalized notion of matching in a simplicial complex and circuits of vector configurations, we compute lower bounds for the minimum number of generators, the binomial arithmetical rank and the A-homogeneous arithmetical rank of a lattice ideal. Prime lattice ideals are toric ideals, i.e. the defining ideals of toric varieties. © 2006 Elsevier Inc. All rights reserved.

in this paper, we introduce a method by which we can find a close connection between the set of prime $z$-ideals of $c(x)$ and the same of $c(y)$, for some special subset $y$ of $x$. for instance, if $y=coz(f)$ for some $fin c(x)$, then there exists a one-to-one correspondence between the set of prime $z$-ideals of $c(y)$ and the set of prime $z$-ideals of $c(x)$ not containing $f$. moreover, c...

In a previous paper we exhibited the somewhat surprising property that most direct links of prime ideals in Gorenstein rings are equimultiple ideals with reduction number 1. This led to the construction of large families of Cohen–Macaulay Rees algebras. The first goal of this paper is to extend this result to arbitrary Cohen–Macaulay rings. The means of the proof are changed since one cannot de...