Ranks of indecomposable modules over rings of infinite Cohen-Macaulay type

Details Ranks of indecomposable modules over rings of infinite Cohen-Macaulay type Ranks of indecomposable modules over rings of infinite Cohen-Macaulay type

2012-01-16

arxiv.org/abs/1201.3141v1

Mathematics

Commutative Algebra

14 pages, submitted

Scientific paper

Let (R,m,k) be a one-dimensional analytically unramified local ring with minimal prime ideals P_1,...,P_s. Our ultimate goal is to study the direct-sum behavior of maximal Cohen-Macaulay modules over R. Such behavior is encoded by the monoid C(R) of isomorphism classes of maximal Cohen-Macaulay R-modules: the structure of this monoid reveals, for example, whether or not every maximal Cohen-Macaulay module is uniquely a direct sum of indecomposable modules; when uniqueness does not hold, invariants of this monoid give a measure of how badly this property fails. The key to understanding the monoid C(R) is determining the ranks of indecomposable maximal Cohen-Macaulay modules. Our main technical result shows that if R/P_1 has infinite Cohen-Macaulay type and the residue field k is infinite, then there exist |k| pairwise non-isomorphic indecomposable maximal Cohen-Macaulay R-modules of rank (r_1,...,r_s) provided r_1 is greater than or equal to r_i for all i. This result allows us to describe the monoid C(R) when all analytic branches of R have infinite Cohen-Macaulay.

Affiliated with

Also associated with

No associations

Rating

Ranks of indecomposable modules over rings of infinite Cohen-Macaulay type does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Ranks of indecomposable modules over rings of infinite Cohen-Macaulay type, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ranks of indecomposable modules over rings of infinite Cohen-Macaulay type will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-409409