R.G. and Perez proved that under certain conditions the test ideal of a module closure agrees with trace closure. We use this fact to compute ideals various rings respect closures coming from their indecomposable maximal Cohen–Macaulay modules. also give an easier way hypersurface ring in three variables particular type matrix factorization.

Björner and Wachs generalized the definition of shellability by dropping the assumption of purity; they also introduced the h-triangle, a doubly-indexed generalization of the h-vector which is combinatorially significant for nonpure shellable complexes. Stanley subsequently defined a nonpure simplicial complex to be sequentially Cohen-Macaulay if it satisfies algebraic conditions that generaliz...

et  be a commutative Noetherian ring,  and  two ideals of  and  a finite -module. In this paper, we have studied the vanishing and relative Cohen-Macaulyness of the functor for relative Cohen-Macauly filtered modules with respect to the ideal  (RCMF). We have shown that the for relative Cohen-Macaulay modules holds for any relative Cohen-Macauly module with respect to  with ........

Let S be an unramified regular local ring having mixed characteristic p > 0 and R the integral closure of S in a pth root extension of its quotient field. We show that R admits a finite, birational module M such that depth(M) = dim(R). In other words, R admits a maximal Cohen-Macaulay module.

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...

We study one-dimensional Cohen-Macaulay rings whose trace ideal of the canonical module is as small possible. In this paper we call such far-flung Gorenstein rings. investigate in relation with endomorphism algebras maximal ideals and numerical semigroup show that solution Rohrbach problem additive number theory provides an upper bound for multiplicity Reflexive modules over are also studied.