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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An invariant for modules over a discrete valuation ring


Author: R. O. Stanton
Journal: Proc. Amer. Math. Soc. 49 (1975), 51-54
MathSciNet review: 0360572
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Abstract | References | Additional Information

Abstract: Warfield has recently defined a new class of invariants for mixed modules over a discrete valuation ring. These invariants, along with the Ulm invariants, enable Warfield to prove an analogue to Ulm's theorem. Warfield's definition contains two shortcomings. The invariants are defined for a limited class of modules. Moreover it is difficult to show that the invariants are well defined. This paper defines a new invariant which coincides with that of Warfield, and overcomes both difficulties.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0360572-8
PII: S 0002-9939(1975)0360572-8
Keywords: Discrete valuation ring, module of torsion free rank one, height sequence
Article copyright: © Copyright 1975 American Mathematical Society