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 Free Access

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?)

  • Nathan Jacobson, Structure of rings, American Mathematical Society Colloquium Publications, Vol. 37, American Mathematical Society, 190 Hope Street, Prov., R. I., 1956. MR 0081264
  • Irving Kaplansky, Infinite abelian groups, University of Michigan Press, Ann Arbor, 1954. MR 0065561
  • Wolfgang Liebert, Endomorphism rings of abelian $p$-groups, Studies on Abelian Groups (Symposium, Montpellier, 1967) Springer, Berlin, 1968, pp. 239–258. MR 0242946
  • 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 310018
  • 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
  • R. S. Pierce, Endomorphism rings of primary Abelian groups, Proc. Colloq. Abelian Groups (Tihany, 1963) Akadémiai Kiadó, Budapest, 1964, pp. 125–137. MR 0172922
  • Kenneth G. Wolfson, An ideal-theoretic characterization of the ring of all linear transformations, Amer. J. Math. 75 (1953), 358–386. MR 53080, DOI

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 <IMG WIDTH="19" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$J$">-finite topology on endomorphism rings
Article copyright: © Copyright 1972 American Mathematical Society