Big projective modules over noetherian semilocal rings
-
Dolors Herbera
and
Pavel Příhoda
Abstract
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 (ℕ0 ∪ {∞})k of a system consisting of congruences and diophantine linear equations. The converse also holds, that is, if M is a submonoid of (ℕ0 ∪ {∞})k containing an order unit (n1, . . . , nk) of 
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) ≅ Mn1(D1) × ⋯ × Mnk (Dk) for suitable division rings D1, . . . , Dk.
© Walter de Gruyter Berlin · New York 2010
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- In memoriam Ernst Steinitz (1871–1928)
- Kuga-Satake abelian varieties of K3 surfaces in mixed characteristic
- Knotted holomorphic discs in
- Smoothness of Lipschitz minimal intrinsic graphs in Heisenberg groups , n > 1
- Big projective modules over noetherian semilocal rings
- On Néron-Raynaud class groups of tori and the capitulation problem
- Weil restriction and support varieties
- Smooth toric Deligne-Mumford stacks
Articles in the same Issue
- In memoriam Ernst Steinitz (1871–1928)
- Kuga-Satake abelian varieties of K3 surfaces in mixed characteristic
- Knotted holomorphic discs in
- Smoothness of Lipschitz minimal intrinsic graphs in Heisenberg groups , n > 1
- Big projective modules over noetherian semilocal rings
- On Néron-Raynaud class groups of tori and the capitulation problem
- Weil restriction and support varieties
- Smooth toric Deligne-Mumford stacks
