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Decompositions of modules over a discrete valuation ring

Part of: Local rings and semilocal rings Theory of modules and ideals

Published online by Cambridge University Press:  09 April 2009

Robert O. Stanton
Robert O. Stanton
Affiliation:
Department of Mathematics and Computer ScienceSt John's University Jamaica, N.Y. 11439, USA
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Abstract

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Let N be a direct summand of a module which is a direct sum of modules of torsion-free rank one over a discrete valuation ring. Then there is a torsion module T such that N⊕T is also a direct sum of modules of torsion-free rank one.

MSC classification

Secondary: 13C05: Structure, classification theorems 13H99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 27 , Issue 3 , May 1979 , pp. 284 - 288
Copyright
Copyright © Australian Mathematical Society 1979

References

Fuchs, L. (1973), Infinite Abelian groups, Vol. II (Academic Press, New York).Google Scholar
MacLane, S. (1967), Homology (Springer-Verlag, New York).Google Scholar
Rotman, J. and Yen, T. (1961), ‘Modules over a complete discrete valuation ring’, Trans. Amer. Math. Soc. 98, 242–254.CrossRefGoogle Scholar
Stanton, R. O. (1973), The A-exchange property applied to decompositions of modules over a discrete valuation ring (doctoral dissertation, New Mexico State University, Las Cruces).Google Scholar
Stanton, R. O. (1975), ‘An invariant for modules over a discrete valuation ring’, Proc. Amer. Math. Soc. 49, 51–54.CrossRefGoogle Scholar
Walker, C. L. and Warfield, R. B. Jr (1976), ‘Unique decomposition and isomorphic refinement theorems in additive categories’, J. Pure Appl. Algebra. 7 347–359.CrossRefGoogle Scholar
Walker, E. A. (1974), ‘Remarks on T*-modules’ (abstract), Notices Amer. Math. Soc. 21, A99.Google Scholar
Wallace, K. D. (1971), ‘On mixed groups of torsion free rank one with totally projective primary components’, J. Algebra 17, 482–488.CrossRefGoogle Scholar
Warfield, R. B. Jr (1975), ‘Classification theory of Abelian groups II, Local theory’, to appear.CrossRefGoogle Scholar