Given a local Noetherian ring (R, m) of dimension d > 0 and infinite residue field, we study the invariants (dimension and multiplicity) of the Sally module SJ (I) of any m-primary ideal I with respect to a minimal reduction J. As a by-product we obtain an estimate for the Hilbert coefficients of m that generalizes a bound established by J. Elias and G. Valla in a local Cohen-Macaulay setting. ...

Over a $d$-dimensional Cohen-Macaulay local ring admitting canonical module the definable closure of class balanced big modules is $d$-cotilting and smallest such containing maximal modules. We describe its cotilting structure contrast it to largest The enables an implicit classification all classes

Let I be a divisorial ideal of a strongly F-regular ring A. K.-i.Watanabe raised thequestionwhether the symbolicRees algebraRs(I) = ⊕n≥0I is Cohen-Macaulay whenever it is Noetherian. We develop the notion ofmulti-symbolic Rees algebras and use this to show thatRs(I) is indeedCohen-Macaulaywhenever a certain auxiliary ring is finitely generated over A.

We investigate the Cohen-Macaulay property for rings of invariants under multiplicative actions of a finite group G. By definition, these are G-actions on Laurent polynomial algebras k[x 1 , . . . , x ±1 n ] that stabilize the multiplicative group consisting of all monomials in the variables xi. For the most part, we concentrate on the case where the base ring k is Z. Our main result states tha...

Let G be a simple undirected graph on n vertices, and let I(G) ⊆ R = k[x1, . . . , xn] denote its associated edge ideal. We show that all chordal graphs G are sequentially Cohen-Macaulay; our proof depends upon showing that the Alexander dual of I(G) is componentwise linear. Our result complements Faridi’s theorem that the facet ideal of a simplicial tree is sequentially Cohen-Macaulay and impl...

This paper studies Frobenius powers of parameter ideals in a commutative Noetherian local ring R of prime characteristic p. For a given ideal a of R, there is a power Q of p, depending on a, such that the Q-th Frobenius power of the Frobenius closure of a is equal to the Q-th Frobenius power of a. The paper addresses the question as to whether there exists a uniform Q0 which ‘works’ in this con...

We investigate Sharifan and Moradi’s closed neighborhood ideal of a finite simple graph, which is square-free monomial in polynomial ring over field. explicitly describe the minimal irreducible decompositions these ideals. also characterize trees whose ideals are Cohen–Macaulay; particular, this property for characteristic independent.

Various classification theorems of thick subcategories of a triangulated category have been obtained in many areas of mathematics. In this paper, as a higher dimensional version of the classification theorem of thick subcategories of the stable category of finitely generated representations of a finite p-group due to Benson, Carlson and Rickard, we consider classifying thick subcategories of th...

The notion of the Cousin complex of a module was given by Sharp in 1969. It wasn’t known whether its cohomologies are finitely generated until recently. In 2001, Dibaei and Tousi showed that the Cousin cohomologies of a finitely generated A-module M are finitely generated if the base ring A is local, has a dualizing complex, M satisfies Serre’s (S2)-condition and is equidimensional. In the pres...