An invariant for modules over a discrete valuation ring

Stanton, R. O.

doi:10.1090/S0002-9939-1975-0360572-8

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An invariant for modules over a discrete valuation ring
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by R. O. Stanton

Proc. Amer. Math. Soc. 49 (1975), 51-54

DOI: https://doi.org/10.1090/S0002-9939-1975-0360572-8

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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.

References

R. B. Warfield Jr., Classification theorems for $p$-groups and modules over a discrete valuation ring, Bull. Amer. Math. Soc. 78 (1972), 88–92. MR 291284, DOI 10.1090/S0002-9904-1972-12870-2

Bibliographic Information

Journal: Proc. Amer. Math. Soc. 49 (1975), 51-54
DOI: https://doi.org/10.1090/S0002-9939-1975-0360572-8
MathSciNet review: 0360572