×

A class of torsion-free abelian groups characterized by the ranks of their socles. (English) Zbl 1013.13007

Summary: Butler groups formed by factoring a completely decomposable group by a rank one group have been studied extensively. We call such groups bracket groups. We study bracket modules over integral domains. In particular, we are interested in when any bracket \(R\)-module is \(R\) tensor a bracket group.

MSC:

13C13 Other special types of modules and ideals in commutative rings
20K15 Torsion-free groups, finite rank
13G05 Integral domains
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] D. A. Arnold: Finite Rank Torsion-Free Abelian Groups and Rings, LNM 931. Springer-Verlag, 1982.
[2] D. M. Arnold and C. I. Vinsonhaler: Finite rank Butler groups, a survey of recent results. Abelian Groups. Lecture Notes in Pure and Appl. Math. 146, Marcel Dekker, 1993, pp. 17-42. · Zbl 0804.20043
[3] U. F. Albrecht and H. P. Goeters: Butler theory over Murley groups. J. Algebra 200 (1998), 118-133. · Zbl 0898.20033 · doi:10.1006/jabr.1997.7211
[4] L. Fuchs and C. Metelli: On a class of Butler groups. Manuscripta Math. 71 (1991), 1-28. · Zbl 0765.20026 · doi:10.1007/BF02568390
[5] H. P. Goeters: An extension of Warfield duality for abelian groups. J. Algebra 180 (1996), 848-861. · Zbl 0845.20042 · doi:10.1006/jabr.1996.0097
[6] H. P. Goeters and Ch. Megibben: Quasi-isomorphism invariants and \({\mathbb{Z}}_2\)-representations for a class of Butler groups. Rendiconte Sem. Mat. Univ. of Padova
[7] H. P. Goeters, W. Ullery and Ch. Vinsonhaler: Numerical invariants for a class of Butler groups. Contemp. Math. 171 (1994), 159-172. · Zbl 0820.20063 · doi:10.1090/conm/171/01771
[8] P. Hill and C. Megibben: The classification of certain Butler groups. J. of Algebra 160 (2) (1993), 524-551. · Zbl 0809.20047 · doi:10.1006/jabr.1993.1199
[9] W. Y. Lee: Codiagonal Butler groups. Chinese J. Math. 17 (1989), 259-271.
[10] E. Matlis: Torsion-Free Modules. University of Chicago Press, 1972. · Zbl 0298.13001
[11] H. Matsumura: Commutative Ring Theory. Cambridge University Press, 1980. · Zbl 0441.13001
[12] F. Richman: An extension of the theory of completely decomposable torsion-free abelian groups. Trans. Amer. Math. Soc. 279 (1983), 175-185. · Zbl 0524.20028 · doi:10.2307/1999377
[13] J. J. Rotman: An Introduction to Homological Algebra. Academic Press, 1979. · Zbl 0441.18018
[14] R. B. Warfield: Homomorphisms and duality for abelian groups. Math. Z. 107 (1968), 189-212. · Zbl 0169.03602 · doi:10.1007/BF01110257
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.