Related papers: A criterion for sequential Cohen-Macaulayness

Let $K$ be a field, $S=K[x_1,\ldots,x_m, y_1,\ldots,y_n]$ be a standard bigraded polynomial ring and $M$ a finitely generated bigraded $S$-module. In this paper we study sequentially Cohen--Macaulayness of $M$ with respect to…

Let $K$ be a field and $S=K[x_1,\ldots,x_m, y_1,\ldots,y_n]$ be the standard bigraded polynomial ring over $K$. In this paper, we explicitly describe the structure of finitely generated bigraded "sequentially Cohen--Macaulay" $S$-modules…

Let $(R, \frak m)$ be a homomorphic image of a Cohen-Macaulay local ring and $M$ a finitely generated $R$-module. We use the splitting of local cohomology to shed a new light on the structure of non-Cohen-Macaulay modules. Namely, we show…

We introduce the notions of sequential sequence and sequential f-sequence in order to characterize sequentially Cohen-Macaulay modules and sequentially generalized Cohen-Macaulay modules. Let R be a Noetherian local ring and M a finitely…

A finitely generated module $M$ over a local ring is called a sequentially generalized Cohen-Macaulay module if there is a filtration of submodules of $M$: $M_0\subset M_1\subset ... \subset M_t=M$ such that $\dim M_0<\dim M_1< >... <\dim…

We establish an inequality relating the projective dimension of a DG-module in $\mathrm{D}^\mathrm{b}_\mathrm{f}(A)$ to its grade and introduce the concept of perfect DG-modules as a natural generalization of perfect modules. It is proved…

This paper shows that if $R$ is a homomorphic image of a Cohen-Macaulay local ring, then $R$-module $M$ is sequentially generalized Cohen-Macaulay if and only if the difference between Hilbert coefficients and arithmetic degrees for all…

It is shown that a module is sequentially Cohen-Macaulay if and only if the index of reducibility for distinguished parameter ideals are eventually constant with special value. As corollaries to the main theorem we given to characterize the…

In this survey paper we first present the main properties of sequentially Cohen-Macaulay modules. Some basic examples are provided to help the reader with quickly getting acquainted with this topic. We then discuss two generalizations of…

We let R be a one-dimensional graded complete intersection, satisfying certain degree conditions which are satisfied whenever R is a numerical semigroup ring of embedding dimension at least three. We show that a graded maximal…

Let $S=K[x_1, \dots, x_m, y_1, \dots, y_n]$ be the standard bigraded polynomial ring over a field $K$. Let $M$ be a finitely generated bigraded $S$-module and $Q=(y_1, \dots, y_n)$. We say $M$ has maximal depth with respect to $Q$ if there…

The purpose of this paper is to present a characterization of sequentially Cohen-Macaulay modules in terms of its Hilbert coefficients with respect to distinguished parameter ideals. The formulas involve arithmetic degrees. Among…

Let \fa be an ideal of a local ring (R,\fm) and M a finitely generated R-module. This paper concerns the notion \fgrade(\fa,M), the formal grade of M with respect to \fa (i.e. the least integer i such that {\vpl}_nH^i_{\fm}(M/\fa^n M)\neq…

We show that the property of a standard graded algebra R being Cohen-Macaulay is characterized by the existence of a pure Cohen-Macaulay R-module corresponding to any degree sequence of length at most depth(R). We also give a relation in…

Let $M$ be an $R$-module over a Noetherian ring $R$ and $\mathfrak{a}$ be an ideal of $R$ with $c={\rm cd}(\mathfrak{a},M)$. First, we prove that $M$ is finite $\mathfrak{a}$-relative Cohen-Macaulay if and only if ${\rm…

Let k be an algebraically closed field and A be a finitely generated, centrally finite, non- negatively graded (not necessarily commutative) k-algebra. In this note we construct a representation scheme for graded maximal Cohen-Macaulay A…

Let $A = K[[X_1,\cdots,X_n]]$ and let $\mathfrak{m} = (X_1,\cdots,X_n)$. Let $M$ be a Cohen-Macaulay $A$-module of codimension $p$. In this paper we give a necessary and sufficient condition for the associated graded module…

The main result of the paper states that for a graded ideal I in a polynomial ring R over a field of characteristic 0, the Hilbert functions of the local cohomology modules of R/I and of R/Gin(I) coincide if and only if R/I is sequentially…

In this paper we present characterizations of sequentially Cohen-Macaulay modules in terms of systems of parameters, which are generalizations of well-known results on Cohen-Macaulay and generalized Cohen-Macaulay modules. The sequentially…

We introduce a notion of degenerations of graded modules. In relation to it, we also introduce several partial orders as graded analogies of the hom order, the degeneration order and the extension order. We prove that these orders are…