Weakly based modules over Dedekind domains

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Weakly based modules over Dedekind domains
Original language description
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(
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
<a href="/en/project/GA201%2F09%2F0816" target="_blank" >GA201/09/0816: Algebraic Methods in the Representation Theory (Approximations, Realizations, and Constraints)</a><br>
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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