Geodesic
DUO MODULES
Glasgow mathematical journal, Tome 48 (2006) no. 3, pp. 533-545

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DOI

Let $R$ be a ring. An $R$-module $M$ is called a (weak) duo module provided every (direct summand) submodule of $M$ is fully invariant. It is proved that if $R$ is a commutative domain with field of fractions $K$ then a torsion-free uniform $R$-module is a duo module if and only if every element $k$ in $K$ such that $kM$ is contained in $M$ belongs to $R$. Moreover every non-zero finitely generated torsion-free duo $R$-module is uniform. In addition, if $R$ is a Dedekind domain then a torsion $R$-module is a duo module if and only if it is a weak duo module and this occurs precisely when the $P$-primary component of $M$ is uniform for every maximal ideal $P$ of $R$.
DOI : 10.1017/S0017089506003260
Mots-clés : 16D99, 13C12 (13B20) 
ÖZCAN, A. Ç.; HARMANCI, A.; SMITH, P. F. DUO MODULES. Glasgow mathematical journal, Tome 48 (2006) no. 3, pp. 533-545. doi: 10.1017/S0017089506003260
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     title = {DUO {MODULES}},
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     pages = {533--545},
     year = {2006},
     volume = {48},
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     doi = {10.1017/S0017089506003260},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089506003260/}
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