Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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] N. Jacobson, Structure of rings, Amer. Math. Soc. Colloq. Publ., vol. 37, Amer. Math. Soc., Providence, R. I., 1956. MR 18, 373. MR 0081264 (18:373d)
  • [2] I. Kaplansky, Infinite abelian groups, Univ. of Michigan Press, Ann Arbor, Mich., 1954. MR 16, 444. MR 0065561 (16:444g)
  • [3] W. Liebert, Endomorphism rings of abelian $ p$-groups, Studies on Abelian Groups (Sympos., Montpellier, 1967), Springer, Berlin, 1968, pp. 239-258. MR 39 #4273. MR 0242946 (39:4273)
  • [4] -, Characterization of the endomorphism rings of the divisible torsion modules and reduced complete torsion-free modules over complete discrete valuation rings, Pacific J. Math. 37 (1971), 141-170. MR 0310018 (46:9121)
  • [5] R. S. Pierce, Homomorphisms of primary abelian groups, Topics in Abelian Groups (Proc. Sympos., New Mexico State Univ., 1962), Scott, Foresman, Chicago, Ill., 1963. MR 31 #1299. MR 0177035 (31:1299)
  • [6] -, 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)
  • [7] K. G. Wolfson, An ideal-theoretic characterization of the ring of all linear transformations, Amer. J. Math. 75 (1953), 358-386. MR 14, 718. MR 0053080 (14:718f)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 16A64

Retrieve articles in all journals with MSC: 16A64

Additional Information

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

American Mathematical Society