On completely decomposable and separable modules over Prüfer domains
László Fuchs and Jorge E. Macías-Díaz
Source: J. Commut. Algebra Volume 2, Number 2
(2010), 159-176.
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Keywords: Torsion-free module; completely decomposable; finitely decomposable and separable module; homogeneously decomposable; type of a rank 1 module; pure; ${\rm RD}$- and ${\rm RD*}$-submodule; $H(\aleph_0)$ and $G(\aleph_0)$-family of submodules; continuous well-ordered ascending chain of modules; $h$-local Prüfer domain
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Permanent link to this document: http://projecteuclid.org/euclid.jca/1275403635
Digital Object Identifier: doi:10.1216/JCA-2010-2-2-159
Mathematical Reviews number (MathSciNet): MR2647473
References
R. Baer, Abelian groups without elements of finite order, Duke Math. J. 3 (1937), 68-122.
Mathematical Reviews (MathSciNet): MR1545974
Digital Object Identifier: doi:10.1215/S0012-7094-37-00308-9
Project Euclid: euclid.dmj/1077489919
T. Chao, Ultrabalanced subgroups of torsion-free abelian groups, Ph.D. Thesis, Tulane University, 1994.
A.L.S. Corner, A note on rank and direct decompositions of torsion-free abelian groups. II, Proc. Cambridge Philos. Soc. 66 (1969), 239-240.
Mathematical Reviews (MathSciNet): MR245670
Digital Object Identifier: doi:10.1017/S0305004100044911
M. Dugas and K.M. Rangaswamy, Separable pure subgroups of completely decomposable torsion-free abelian groups, Arch. Math. 58 (1992), 332-337.
Mathematical Reviews (MathSciNet): MR1152619
Zentralblatt MATH: 0789.20061
Digital Object Identifier: doi:10.1007/BF01189921
L. Fuchs, Infinite abelian groups, Vol 2, Academic Press, New York, 1973.
Mathematical Reviews (MathSciNet): MR349869
Zentralblatt MATH: 0257.20035
L. Fuchs and P. Hill, The balanced-projective dimension of abelian $p$-groups, Trans. Amer. Math. Soc. 293 (1986), 99-112.
Mathematical Reviews (MathSciNet): MR814915
Zentralblatt MATH: 0602.20047
Digital Object Identifier: doi:10.2307/2000274
JSTOR: links.jstor.org
L. Fuchs and L. Salce, Modules over non-Noetherian Domains, Math. Surveys Mono. 84, American Mathematical Society, Providence, 2001.
Mathematical Reviews (MathSciNet): MR1794715
Zentralblatt MATH: 0973.13001
L. Fuchs and G. Viljoen, Completely decomposable pure subgroups of completely decomposable abelian groups, Rend. Sem. Mat. Univ. Padova 92 (1994), 63-69.
Mathematical Reviews (MathSciNet): MR1320479
P. Goeters, When summands of completely decomposable modules are completely decomposable, Comm. Algebra 35 (2007), 1956-1970.
Mathematical Reviews (MathSciNet): MR2324626
Zentralblatt MATH: 1123.13008
Digital Object Identifier: doi:10.1080/00927870701247088
P. Hill, On the freeness of abelian groups: A generalization of Pontryagin�s theorem, Bull. Amer. Math. Soc. 76 (1970), 1118-1120.
Mathematical Reviews (MathSciNet): MR263919
Zentralblatt MATH: 0223.20058
Digital Object Identifier: doi:10.1090/S0002-9904-1970-12586-1
Project Euclid: euclid.bams/1183532228
I. Kaplansky, Projective modules, Ann. Math. 68 (1938), 372-377.
Mathematical Reviews (MathSciNet): MR100017
Digital Object Identifier: doi:10.2307/1970252
JSTOR: links.jstor.org
G. Kolettis, Jr., Homogeneously decomposable modules, in Studies in abelian groups, Dunod, Paris, 1968%, 223-238.
Mathematical Reviews (MathSciNet): MR244228
Zentralblatt MATH: 0213.30802
J.E. Macias Diaz, Projectivity and complete decomposability of modules over domains, Ph.D. thesis, Tulane University, 2001.
W.W. McGovern, G. Puninski and P. Rothmaler, When every projective module is a direct sum of finitely generated modules, J. Algebra 31 (2007), 454-481.
Mathematical Reviews (MathSciNet): MR2344352
Zentralblatt MATH: 1126.13008
Digital Object Identifier: doi:10.1016/j.jalgebra.2007.01.043
B. Olberding, Prüfer domains and pure submodules of direct sums of ideals, Mathematika 46 (1999), 425-432.
Mathematical Reviews (MathSciNet): MR1832633
Digital Object Identifier: doi:10.1112/S0025579300007889
K.M. Rangaswamy, A criterion for complete decomposability and Butler modules over valuation domains, J. Algebra 205 (1988), 105-118.
Mathematical Reviews (MathSciNet): MR1631322
Zentralblatt MATH: 0941.13012
Digital Object Identifier: doi:10.1006/jabr.1997.7398
Journal of Commutative Algebra