Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

Homological dimension of abelian groups over their endomorphism rings


Authors: Fred Richman and Elbert A. Walker
Journal: Proc. Amer. Math. Soc. 54 (1976), 65-68
DOI: https://doi.org/10.1090/S0002-9939-1976-0393279-2
MathSciNet review: 0393279
Full-text PDF Free Access

Abstract | References | Additional Information

Abstract: The projective dimension of an abelian group with torsion reduced part, as a module over its endomorphism ring, is determined. In particular, a group of projective dimension $ 2$ is exhibited.


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

  • [1] H. Cartan and S. Eilenberg, Homological algebra, Princeton Univ. Press, Princeton, N. J., 1956. MR17, 1040. MR 0077480 (17:1040e)
  • [2] A. J. Douglas and H. K. Farahat, The homological dimension of an Abelian group as a module over its ring of endomorphisms, Monatsh. Math. 69(1965), 294-305. MR32 #2473. MR 0185002 (32:2473)
  • [3] -, The homological dimension of an abelian group as a module over its ring of endomorphisms. II, Monatsh. Math. 76(1972), 109-111. MR47 #3568. MR 0315019 (47:3568)
  • [4] L. Fuchs, Infinite abelian groups. Vols. I, II. Pure and Appl. Math., vol. 36, Academic Press, New York, 1970, 1973. MR41 #333.
  • [5] D. G. Northcott, An introduction to homological algebra, Cambridge Univ. Press, New York, 1960. MR22 #9523. MR 0118752 (22:9523)
  • [6] F. Richman and E. A. Walker, Primary abelian groups as modules over their endomorphism rings, Math. Z. 89(1965), 77-81. MR32 #2475. MR 0185004 (32:2475)
  • [7] -, Modules over PID's that are injective over their endomorphism rings, Ring Theory, edited by R. Gordon, Academic Press, New York, 1972, pp. 363-372. MR 0354780 (50:7257)
  • [8] R. B. Warfield, Jr., An isomorphic refinement theorem for abelian groups, Pacific J. Math. 34(1970), 237-255. MR42 #1896. MR 0266994 (42:1896)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0393279-2
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society