Weakly based modules over Dedekind domains

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10287247" target="_blank" >RIV/00216208:11320/14:10287247 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.jalgebra.2013.09.031" target="_blank" >http://dx.doi.org/10.1016/j.jalgebra.2013.09.031</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jalgebra.2013.09.031" target="_blank" >10.1016/j.jalgebra.2013.09.031</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Weakly based modules over Dedekind domains

Popis výsledku v původním jazyce

We say that a subset X of a left R-module M is weakly independent provided that whenever a(1)x(1) + ... + a(n)x(n) = 0 for pairwise distinct elements x(1), ... , x(n) form X, then none of a(1), ... , a(n) is invertible in R. Weakly independent generatingsets (we call them weak bases) are exactly generating sets minimal with respect to inclusion. The aim of the paper is to characterize modules over Dedekind domains possessing a weak basis. We will characterize them as follows: Let R be a Dedekind domainand let M be a x-generated R-module, for some infinite cardinal x. Then M has a weak basis iff at least one of the following conditions is satisfied: (1) There are two different prime ideals P, Q of R such that dim(R/P) (M/PM) = dim(R/Q) (M/QM) = x; (2)There are a prime ideal P of R and a decomposition M similar or equal to F circle plus N where F is a free module and dim(R/P) (tau N/P tau N) = gen(N); (3) There is a projection of M onto an R-module circle plus(P is an element of Spec(

Název v anglickém jazyce

Weakly based modules over Dedekind domains

Popis výsledku anglicky

We say that a subset X of a left R-module M is weakly independent provided that whenever a(1)x(1) + ... + a(n)x(n) = 0 for pairwise distinct elements x(1), ... , x(n) form X, then none of a(1), ... , a(n) is invertible in R. Weakly independent generatingsets (we call them weak bases) are exactly generating sets minimal with respect to inclusion. The aim of the paper is to characterize modules over Dedekind domains possessing a weak basis. We will characterize them as follows: Let R be a Dedekind domainand let M be a x-generated R-module, for some infinite cardinal x. Then M has a weak basis iff at least one of the following conditions is satisfied: (1) There are two different prime ideals P, Q of R such that dim(R/P) (M/PM) = dim(R/Q) (M/QM) = x; (2)There are a prime ideal P of R and a decomposition M similar or equal to F circle plus N where F is a free module and dim(R/P) (tau N/P tau N) = gen(N); (3) There is a projection of M onto an R-module circle plus(P is an element of Spec(

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

<a href="/cs/project/GA201%2F09%2F0816" target="_blank" >GA201/09/0816: Algebraické metody teorie reprezentací (aproximace, realizace a omezení)</a><br>

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

Journal of Algebra

ISSN

0021-8693

e-ISSN

—

Svazek periodika

2014

Číslo periodika v rámci svazku

399

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

18

Strana od-do

251-268

Kód UT WoS článku

000330006200013

EID výsledku v databázi Scopus

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