Criteria for flatness and injectivity

Details Criteria for flatness and injectivity Criteria for flatness and injectivity

2011-03-24

arxiv.org/abs/1103.4726v1

Mathematics

Commutative Algebra

19 pages

Scientific paper

Let $R$ be a commutative Noetherian ring. We give criteria for flatness of $R$-modules in terms of associated primes and torsion-freeness of certain tensor products. This allows us to develop a criterion for regularity if $R$ has characteristic $p$, or more generally if it has a locally contracting endomorphism. Dualizing, we give criteria for injectivity of $R$-modules in terms of coassociated primes and (h-)divisibility of certain $\Hom$-modules. Along the way, we develop tools to achieve such a dual result. These include a careful analysis of the notions of divisibility and h-divisibility (including a localization result), a theorem on coassociated primes across a $\Hom$-module base change, and a local criterion for injectivity.

Affiliated with

Also associated with

No associations

Rating

Criteria for flatness and injectivity 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 Criteria for flatness and injectivity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Criteria for flatness and injectivity will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-47488