INFINITELY GENERATED PROJECTIVE MODULES OVER PULLBACKS OF RINGS

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10288465" target="_blank" >RIV/00216208:11320/14:10288465 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
INFINITELY GENERATED PROJECTIVE MODULES OVER PULLBACKS OF RINGS
Original language description
We use pullbacks of rings to realize the submonoids M of (N-0 boolean OR {infinity})(k), which are the set of solutions of a finite system of linear diophantine inequalities as the monoid of isomorphism classes of countably generated projective right R-modules over a suitable semilocal ring. For these rings, the behavior of countably generated projective left R-modules is determined by the monoid D(M) defined by reversing the inequalities determining the monoid M. These two monoids are not isomorphic ingeneral. As a consequence of our results we show that there are semilocal rings such that all its projective right modules are free but this fails for projective left modules. This answers in the negative a question posed by Fuller and Shutters. We alsoprovide a rich variety of examples of semilocal rings having nonfinitely generated projective modules that are finitely generated modulo the Jacobson radical.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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