Big projective modules over noetherian semilocal rings

Mathematics – Rings and Algebras

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

41 pages

Scientific paper

We prove that for a noetherian semilocal ring $R$ with exactly $k$ isomorphism classes of simple right modules the monoid $V^*(R)$ of isomorphism classes of countably generated projective right (left) modules, viewed as a submonoid of $V^*(R/J(R))$, is isomorphic to the monoid of solutions in $(\No \cup\{\infty\})^k$ of a system consisting of congruences and diophantine linear equations. The converse also holds, that is, if $M$ is a submonoid of $(\No \cup\{\infty\})^k$ containing an order unit $(n_1,..., n_k)$ of $\No^k$ which is the set of solutions of a system of congruences and linear diophantine equations then it can be realized as $V^*(R)$ for a noetherian semilocal ring such that $R/J(R)\cong M_{n_1}(D_1)\times ... \times M_{n_k}(D_k)$ for suitable division rings $D_1,..., D_k$.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Big projective modules over noetherian semilocal rings 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 Big projective modules over noetherian semilocal rings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Big projective modules over noetherian semilocal rings will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-491431

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.