In this paper we look at the properties of modules and prime ideals in finite dimensional noetherian rings. This paper is divided into four sections. The first section deals with noetherian one-dimensional rings. Section Two deals with what we define a “zero minimum rings” and explores necessary and sufficient conditions for the property to hold. In Section Three, we come to the minimal prime i...

For every prime integer p, M. Hochster conjectured the existence of certain p-torsion elements in a local cohomology module over a regular ring of mixed characteristic. We show that Hochster’s conjecture is false. We next construct an example where a local cohomology module over a hypersurface has p-torsion elements for every prime integer p, and consequently has infinitely many associated prim...

Lee in 1970 determined the equational subclasses m B of the class of all pseudo complemented lattices. Then many authors have worked with the lattices which are in m B , sectionally in m B and relatively in m B . In this paper we extend some of their results in terms of n-ideals. We will study those ( ) L Fn which are relatively in m B . Here we include a number of characterizations of those ( ...

In west coast groundfish stock assessments, biological productivity is largely defined by a single parameter, i.e., steepness (h) of the Beverton-Holt spawner-recruit curve, which ranges from 0.20 (no compensation) to 1.00 (complete compensation). A steepness of 0.20 implies no latent surplus production and a total lack of resilience to the effects of exploitation, whereas a value of 1.0 implie...

Implementation theory tackles the following problem: given a social choice correspondence, find a decentralized mechanism such that for every constellation of the individuals’ preferences, the set of outcomes in equilibrium is exactly the set of socially optimal alternatives (as specified by the correspondence). In this paper we are concerned with implementation by mediated equilibrium; under s...

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 ...