Let ∆ be a triangulated homology ball whose boundary complex is ∂∆. A result of Hochster asserts that the canonical module of the Stanley–Reisner ring of ∆, F[∆], is isomorphic to the Stanley–Reisner module of the pair (∆, ∂∆), F[∆, ∂∆]. This result implies that an Artinian reduction of F[∆, ∂∆] is (up to a shift in grading) isomorphic to the Matlis dual of the corresponding Artinian reduction ...

First we construct an interesting bijection between the set of h-vectors and the set of socle-vectors of artinian algebras. As a simple consequence, we find the minimum codimension that an artinian algebra with a given socle-vector can have. Then we address the main problem of this paper: determining when there is a unique socle-vector associated to a given h-vector. In Sections 3 and 5 we work...

The notion of interval-valued intuitionistic fuzzy sets was first introduced by Atanassov and Gargov in 1989 as a generalization of both interval-valued fuzzy sets and intuitionistic fuzzy sets. In this paper we first apply the concept of interval-valued intuitionistic fuzzy sets to K-algebras. Then we introduce the notion of interval-valued intuitionistic fuzzy ideals (IIFIs, in short) of K-al...

We investigate the face numbers of simplicial complexes with Buchsbaum vertex links, especially pseudomanifolds with isolated singularities. This includes deriving Dehn-Sommerville relations for pseudomanifolds with isolated singularities and establishing lower and upper bound theorems when the singularities are also homologically isolated. We give formulas for the Hilbert function of a generic...

The aim of this paper is to investigate strong notion strongly ⨁-supplemented modules in module theory, namely ⨁-locally artinian supplemented modules. We call a M if it locally and its supplement submodules are direct summand. In study, we provide the basic properties particular, show that every summand supplemented. Moreover, prove ring R semiperfect with radical only projective R-module