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INDEPENDENTLY GENERATED MODULES
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 Title & Authors
INDEPENDENTLY GENERATED MODULES
Kosan, Muhammet Tamer; Ozdin, Tufan;
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 Abstract
A module M over a ring R is said to satisfy (P) if every generating set of M contains an independent generating set. The following results are proved; (1) Let = () be a hereditary torsion theory such that Mod-R. Then every -torsionfree R-module satisfies (P) if and only if S = R/(R) is a division ring. (2) Let be a hereditary pre-torsion class of modules. Then every module in satisfies (P) if and only if either = {0} or S = R/(R) is a division ring, where (R) = {I : R/I}.
 Keywords
generated set for modules;basis;(non)-singular modules;division ring;torsion theory;
 Language
English
 Cited by
 References
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