let $(r,m)$ be a commutative noetherian local ring, $m$ a finitely generated $r$-module of dimension $d$, and let $i$ be an ideal of definition for $m$. in this paper, we extend cite[corollary 10(4)]{p} and also we show that if $m$ is a cohen-macaulay $r$-module and $d=2$, then $lambda(frac{widetilde{i^nm}}{jwidetilde{i^{n-1}m}})$ does not depend on $j$ for all $ngeq 1$, where $j$ is a minimal ...

Let $(R,m)$ be a commutative Noetherian local ring, $M$ a finitely generated $R$-module of dimension $d$, and let $I$ be an ideal of definition for $M$. In this paper, we extend cite[Corollary 10(4)]{P} and also we show that if $M$ is a Cohen-Macaulay $R$-module and $d=2$, then $lambda(frac{widetilde{I^nM}}{Jwidetilde{I^{n-1}M}})$ does not depend on $J$ for all $ngeq 1$, where $J$ is a minimal ...

In this expository paper we survey results proved during the last fifty years that relate Hilbert coefficients e0(I) and e1(I) of an m-primary ideal I in a Cohen-Macaulay local ring (R, m) with depth of the associated graded ring G(I). Several results in this area follow from two theorems of S. Huckaba and T. Marley. These were proved using homological techniques. We provide simple proofs using...

In this paper, we discuss some necessary and sufficient conditions for a curve to be arithmetically Cohen-Macaulay, in terms of its general hyperplane section. We obtain a characterization of the degree matrices that can occur for points in the plane that are the general plane section of a non arithmetically Cohen-Macaulay curve of P. We prove that almost all the degree matrices with positive s...

Let  be a local Cohen-Macaulay ring with infinite residue field,  an Cohen - Macaulay module and  an ideal of  Consider  and , respectively, the Rees Algebra and associated graded ring of , and denote by  the analytic spread of  Burch’s inequality says that  and equality holds if  is Cohen-Macaulay. Thus, in that case one can compute the depth of associated graded ring of  as  In this paper we ...

The multiplicity conjecture of Herzog, Huneke, and Srinivasan is verified for the face rings of the following classes of simplicial complexes: matroid complexes, complexes of dimension one and two, and Gorenstein complexes of dimension at most four. The lower bound part of this conjecture is also established for the face rings of all doubly Cohen-Macaulay complexes whose 1-skeleton’s connectivi...

Let R be a Cohen-Macaulay ring and M a maximal CohenMacaulay R-module. Inspired by recent striking work by Iyama, BurbanIyama-Keller-Reiten and Van den Bergh we study the question of when the endomorphism ring of M has finite global dimension via certain conditions about vanishing of Ext modules. We are able to strengthen certain results by Iyama on connections between a higher dimension versio...

Let be a commutative Noetherian ring and let I be a proper ideal of . D’Anna and Fontana in [6] introduced a new construction of ring,  named amalgamated duplication of along I. In this paper by considering the ring homomorphism , it is shown that if , then , also it is proved that if , then there exists  such that . Using this result it is shown that if is generically Cohen-Macaulay (resp. gen...