We describe the structure of monoid natural-valued monotone functions on an arbitrary poset. For this we provide a presentation, characterization prime elements, and description its convex hull. also study associated ring, proving that it is normal, thus Cohen-Macaulay. determine Cohen-Macaulay type, characterize Gorenstein property, Gröbner basis defining ideal. Then apply these results to qua...

Let k be an algebraically closed field of characteristic zero, S = k[X0, X1, X2, X3, X4] and P = Proj(S). By a curve we always mean a closed one-dimensional subscheme of P which is locally Cohen-Macaulay and equidimensional. The main purpose of this paper is to show that arithmetically Cohen-Macaulay curves C ⊂ P lying on a “general” arithmetically Cohen-Macaulay surface X ⊂ P with degree matri...

The aim of this paper is to investigate properties of the local cohomology of rings of mixed characteristic that are analogous to Segre products of rings de ned over a eld. The main question is whether the local cohomology can be almost killed in a nite extension (we de ne what this means below). There are two reasons for considering this type of ring. First, there are special properties of the...

We examine some recent work of Phillip Griffith on étale covers and fibered products from the point of view of tight closure theory. While it is known that cyclic covers of Gorenstein rings with rational singularities are Cohen-Macaulay, we show this is not true in general in the absence of the Gorenstein hypothesis. Specifically, we show that the canonical cover of a Q-Gorenstein ring with rat...

We study in detail locally Cohen-Macaulay curves in P 3 which are contained in a double plane 2H , thus completing the classification of curves lying on surfaces of degree two. We describe the irreducible components of the Hilbert schemes Hd,g(2H) of locally Cohen-Macaulay curves in 2H of degree d and arithmetic genus g, and we show that Hd,g(2H) is connected. We also discuss the Rao module of ...

We show that any quasi-Gorenstein deformation of a 3-dimensional Buchsbaum local ring with I-invariant 1 admits maximal Cohen-Macaulay module, provided it is quotient Gorenstein ring. Such class rings includes two instances unique factorization domains constructed by Marcel-Schenzel and Imtiaz-Schenzel, respectively. Apart from this result, motivated the small conjecture in prime characteristic...

s. 1 Let (R,m) be a Noetherian local ring which is a quotient of a Gorenstein local ring. Let M be a finitely generated R-module. In this paper, we study the structure of the canonical module K(RnM) of the idealization RnM via the polynomial type introduced by N. T. Cuong [5]. In particular, we give a characterization for K(RnM) being Cohen-Macaulay and generalized Cohen-Macaulay.

We prove a theorem unifying three results from combinatorial homological and commutative algebra, characterizing the Koszul property for incidence algebras of posets and affine semigroup rings, and characterizing linear resolutions of squarefree monomial ideals. The characterization in the graded setting is via the Cohen-Macaulay property of certain posets or simplicial complexes, and in the mo...

Let R be a local Cohen-Macaulay ring, I an R-ideal and G the associated graded ring of I. We give an estimate for the depth of G when G fails to be Cohen-Macaulay. We assume that I has small reduction number, sufficiently good residual intersection properties, and satisfies local conditions on the depth of some powers. The main theorem unifies and generalizes several known results. We also give...