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Primary modules determined by indecomposable idempotent endomorphisms.


Author: Robert W. Stringall
Journal: Proc. Amer. Math. Soc. 31 (1972), 54-56
DOI: https://doi.org/10.1090/S0002-9939-1972-0285608-1
MathSciNet review: 0285608
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Abstract | References | Additional Information

Abstract: A faithful primary module over a complete discrete valuation ring is determined up to isomorphism by any subring of the endomorphism ring of the module which contains all the indecomposable indempotent endomorphisms.


References [Enhancements On Off] (What's this?)

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  • [2] I. Kaplansky, Infinite abelian groups, rev. ed., Univ. of Michigan Press, Ann Arbor, Mich., 1969. MR 38 #2208. MR 0233887 (38:2208)
  • [3] R. S. Pierce, Endomorphism rings of primary Abelian groups, Proc. Colloq. Abelian Groups (Tihany, 1963), Akad. Kiadó, Budapest, 1964, pp. 125-137. MR 30 #3137. MR 0172922 (30:3137)
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  • [5] R. Stringall, Decompositions of Abelian $ p$-groups, Proc. Amer. Math. Soc. 28 (1971), 409-410. MR 0274582 (43:345)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0285608-1
Keywords: Faithful primary modules over complete discrete valuation rings, subring generated by idempotent endomorphisms, subring generated by automorphisms
Article copyright: © Copyright 1972 American Mathematical Society

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