‎let $m$ be a non-zero finitely generated module over a commutative noetherian local ring $(r,mathfrak{m})$ with $dim_r(m)=t$‎. ‎let $i$ be an ideal of $r$ with $grade(i,m)=c$‎. ‎in this article we will investigate several natural homomorphisms of local cohomology modules‎. ‎the main purpose of this article is to investigate when the natural homomorphisms $gamma‎: ‎tor^{r}_c(k,h^c_i(m))to kotim...

we call a module  essentially retractable if homr for all essential submodules n of m. for a right fbn ring r, it is shown that: (i)  a non-zero module  is retractable (in the sense that homr for all non-zero ) if and only if certain factor modules of m are essentially retractable nonsingular modules over r modulo their annihilators. (ii)  a non-zero module  is essentially retractable if and on...

Exploiting the analogy between exemplar models and population coding schemes, we characterize, by means of information theoretic tools, the efficiency of a large but finite population of cells coding for a discrete set of categories (e.g. vowels). The optimal code is shown to typically allocate more cells to class boundaries than to regions further apart. We then discuss the predicted perceptua...

We consider the problem of designing reliable and confidential lattice codes, known as wiretap lattice codes, for fast fading channels. We identify as code design criterion for finite lattice constellations a finite sum of inverse of algebraic norms, in fact the analogous for finite sums of the known criterion for infinite constellations, which motivates us to study totally real number fields w...

Pregnancy and delivery is one of the main causes in the female body weight alteration, especially with obesity. This alteration in body weight has a significant effect not only for a femine beauty standpoint, but also for more important reproductive functions in postpartum. For the actual condition of the maternal body weight alteration and its clinical significance, we made the various analysi...

To each finitely presented module M over a commutative ring R one can associate an R-ideal FitR(M) which is called the (zeroth) Fitting ideal of M over R and which is always contained in the R-annihilator of M . In an earlier article, the second author generalised this notion by replacing R with a (not necessarily commutative) oorder Λ in a finite dimensional separable algebra, where o is an in...

We call a module  essentially retractable if HomR for all essential submodules N of M. For a right FBN ring R, it is shown that: (i)  A non-zero module  is retractable (in the sense that HomR for all non-zero ) if and only if certain factor modules of M are essentially retractable nonsingular modules over R modulo their annihilators. (ii)  A non-zero module  is essentially retractable if and on...

Let R be a commutative ring with unity, M unitary R-module and G finite abelian group (viewed as \({\mathbb {Z}}\)-module). The main objective of this paper is to study properties mod-annihilators M. For \(x \in M\), we the ideals \([x : M] =\{r\in ~|~ rM\subseteq Rx\}\) corresponding mod-annihilator We investigate when [x an essential ideal R. prove that arbitrary intersection represented by i...

Let A be a Noetherian local ring with the maximal ideal m and an m-primary ideal J . Let F = {In}n≥0 be a good filtration of ideals in A. Denote by FJ (F) = ⊕ n≥0 (In/JIn)t n the fiber cone of F with respect to J. The paper characterizes the multiplicity and the CohenMacaulayness of FJ (F) in terms of minimal reductions of F .

We study the structure of the maximal ideal space M(H∞) of the algebra H ∞ = H∞(D) of bounded analytic functions defined on the open unit disk D ⊂ C. Based on the fact that dim M(H∞) = 2 we prove for H∞ the matrix-valued corona theorem. Our results heavily rely on the topological construction describing maximal ideal spaces of certain algebras of continuous functions defined on the covering spa...