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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Endomorphism rings of reduced torsion-free modules over complete discrete valuation rings

Author: Wolfgang Liebert
Journal: Trans. Amer. Math. Soc. 169 (1972), 347-363
MSC: Primary 16A64
MathSciNet review: 0306268
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Abstract: The purpose of this paper is to find necessary and sufficient conditions that an abstract ring be isomorphic to the ring of all endomorphisms of a reduced torsion-free module over a (possibly noncommutative) complete discrete valuation ring.

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

  • [1] Nathan Jacobson, Structure of rings, American Mathematical Society, Colloquium Publications, vol. 37, American Mathematical Society, 190 Hope Street, Prov., R. I., 1956. MR 0081264
  • [2] Irving Kaplansky, Infinite abelian groups, University of Michigan Press, Ann Arbor, 1954. MR 0065561
  • [3] Wolfgang Liebert, Endomorphism rings of abelian 𝑝-groups, Studies on Abelian Groups (Symposium, Montpellier, 1967) Springer, Berlin, 1968, pp. 239–258. MR 0242946
  • [4] Wolfgang Liebert, Characterization of the endomorphism rings of divisible torsion modules and reduced complete torsion-free modules over complete discrete valuation rings, Pacific J. Math. 37 (1971), 141–170. MR 0310018
  • [5] R. S. Pierce, Homomorphisms of primary abelian groups, Topics in Abelian Groups (Proc. Sympos., New Mexico State Univ., 1962), Scott, Foresman and Co., Chicago, Ill., 1963, pp. 215–310. MR 0177035
  • [6] R. S. Pierce, Endomorphism rings of primary Abelian groups, Proc. Colloq. Abelian Groups (Tihany, 1963) Akadémiai Kiadó, Budapest, 1964, pp. 125–137. MR 0172922
  • [7] Kenneth G. Wolfson, An ideal-theoretic characterization of the ring of all linear transformations, Amer. J. Math. 75 (1953), 358–386. MR 0053080,

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Keywords: Complete discrete valuation ring, reduced torsion-free module, endomorphism ring, finite endomorphisms, Jacobson radical, sum of all minimal nonradical right (left) ideals, finite topology and $ J$-finite topology on endomorphism rings
Article copyright: © Copyright 1972 American Mathematical Society

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