The Index of Reducibility of Parameter Ideals and Mostly Zero Finite Local Cohomologies

The Index of Reducibility of Parameter Ideals in Low Dimension

In this paper we present results concerning the following question: If M is a finitely-generated module with finite local cohomologies over a Noetherian local ring (A,m), does there exist an integer l such that every parameter ideal for M contained in m has the same index of reducibility? We show that the answer is yes if dimM = 1 or if dimM = 2 and depthM > 0. This research is closely related ...

On One-Sided Ideals of Rings of Linear Transformations

A Generalized Hochster’s Formula for Local Cohomologies of Monomial Ideals

The Hilbert series of local cohomologies for monomial ideals, which are not necessarily square-free, is established. As applications, we give a sharp lower bound of the non-vanishing degree of local cohomologies and also a sharp lower bound of the positive integer k of k-Buchsbaumness for generalized CohenMacaulay monomial ideals.

Zero elements and $z$-ideals in modified pointfree topology

‎In this paper‎, ‎we define and study the notion of zero elements in topoframes; a topoframe is a pair‎ ‎$(L‎, ‎tau)$‎, ‎abbreviated $L_{ tau}$‎, ‎consisting of a frame $L$ and a‎ ‎subframe $ tau $ all of whose elements are complemented elements in‎ ‎$L$‎. ‎We show that‎ ‎the $f$-ring $ mathcal{R}(L_tau)$‎, ‎the set of $tau$-real continuous functions on $L$‎, ‎is uniformly complete‎. ‎Also‎, ‎t...

Generalized Complete Intersections with Linear Resolutions

We determine the simplicial complexes ∆ whose Stanley-Reisner ideals I∆ have the following property: for all n ≥ 1 the powers In ∆ have linear resolutions and finite length local cohomologies.