Specialization of modules over a local ring

Uniformly Secondary Modules over Commutative Ring

In [2] the notion of “uniformly ideal” was introduced and developed the basic theory. In this article we introduce and advance a theory which, in a sense, dual to that i.e, the notion of “uniformly secondary module”.

Rigid Resolution of a Finitely Generated Module Over a Regular Local Ring

Construction of Finite Sequences over Ring and Left-, Right-, and Bi-Modules over a Ring

This text includes definitions of finite sequences over rings and left-, right-, and bi-module over a ring, treated as functions defined for all natural numbers, but almost everywhere equal to zero. Some elementary theorems are proved, in particular for each category of sequences the schema of existence is proved. In all four cases, i.e for rings, left-, right-, and bi-modules are almost exactl...

The Cohomology of Modules over a Complete Intersection Ring

We investigate the cohomology of modules over commutative complete intersection rings. The first main result is that if M is an arbitrary module over a complete intersection ring R, and if Ext 2n R (M, M) = 0 for some n ≥ 1 then M has finite projective dimension. The second main result gives a new proof of the fact that the support variety of a Cohen-Macaulay module whose completion is indecomp...

Classifying Subcategories of Modules over a Commutative Noetherian Ring

Abstract. Let R be a quotient ring of a commutative coherent regular ring by a finitely generated ideal. Hovey gave a bijection between the set of coherent subcategories of the category of finitely presented R-modules and the set of thick subcategories of the derived category of perfect R-complexes. Using this isomorphism, he proved that every coherent subcategory of finitely presented R-module...