INFINITELY GENERATED PROJECTIVE MODULES OVER PULLBACKS OF RINGS

Kód výsledku v 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>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

INFINITELY GENERATED PROJECTIVE MODULES OVER PULLBACKS OF RINGS

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

INFINITELY GENERATED PROJECTIVE MODULES OVER PULLBACKS OF RINGS

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2014

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Transactions of the American Mathematical Society

ISSN

0002-9947

e-ISSN

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Svazek periodika

366

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

22

Strana od-do

1433-1454

Kód UT WoS článku

000329123600013

EID výsledku v databázi Scopus

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