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Transactions of the American Mathematical Society

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On quasiprojective covers


Author: Theodore G. Faticoni
Journal: Trans. Amer. Math. Soc. 278 (1983), 101-113
MSC: Primary 16A50; Secondary 13C10
DOI: https://doi.org/10.1090/S0002-9947-1983-0697063-X
MathSciNet review: 697063
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Abstract: The main results determine the Goldie dimension of superfluous submodules of semiprime left Goldie rings and apply this to the study of quasiprojective covers of torsion free modules. Conditions are given to guarantee that a quasiprojective cover of a torsion free module is an isomorphism. A class of nonperfect rings is given such that finitely generated singular modules possess quasiprojective covers.


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  • [1] F. W. Anderson and K. R. Fuller, Rings and categories of modules, Springer, Berlin and New York , 1974. MR 0417223 (54:5281)
  • [2] D. Arnold, Torsion free abelian groups of finite rank and subrings of finite dimensional $ Q$-algebras, Lecture Notes in Math., vol. 931, Springer-Verlag, Berlin and New York, 1982. MR 665251 (84d:20002)
  • [3] D. Arnold, R. Pierce, J. Reid, C. Vinsonhaler and W. Wickless, Torsion free abelian groups of finite rank projective as modules over their endomorphism rings, J. Algebra (to appear). MR 627421 (83a:20074)
  • [4] M. F. Atiyah and I. G. McDonald, Introduction to commutative algebra, Addison-Wesley, Reading, Mass., 1979.
  • [5] H. Bass, Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960), 466-488. MR 0157984 (28:1212)
  • [6] A. W. Chatters and C. R. Hajarnavis, Rings with chain conditions, Pitman, Boston, Mass., 1980. MR 590045 (82k:16020)
  • [7] D. Eisenbud and J. C. Robson, Modules over Dedekind prime rings, Algebra 16 (1970), 67-85. MR 0289559 (44:6747)
  • [8] T. G. Faticoni, On classifying quasi-projective modules, Finitely faithful modules and finitely generated quasi-projective modules, Comm. Algebra (submitted).
  • [9] K. R. Fuller and D. A. Hill, On quasi-projective modules via relative projectivity, Arch. Math. (Basel) 21 (1970), 369-373. MR 0272815 (42:7696)
  • [10] J. Lambek, Lectures on rings and modules, Blaisdell, Waltham, Mass., 1966. MR 0206032 (34:5857)
  • [11] K. M. Rangaswamy, Some remarks on the endomorphism rings of quasi-projective modules (to appear).
  • [12] K. Rangaswamy and N. Vanja, Quasi-projectives in abelian and module categories, Pacific J. Math. 43 (1972), 221-238. MR 0314936 (47:3485)
  • [13] I. Reiner, Maximal orders, Academic Press, New York, 1975. MR 0393100 (52:13910)
  • [14] K. W. Roggenkamp and V. H. Dyson, Lattices over orders. I, Lecture Notes in Math., vol. 115, Springer-Verlag, Berlin and New York, 1970. MR 0283013 (44:247a)
  • [15] K. W. Roggenkamp, Lattices over orders. II, Lecture Notes in Math., vol. 142, Springer-Verlag, Berlin and New York, 1970. MR 0283014 (44:247b)
  • [16] S. Singh, Quasi-injective and quasi-projective modules over hereditary Noetherian prime rings, Canad. J. Math 26 (1974), 1173-1185. MR 0352175 (50:4662)
  • [17] -, Modules over hereditary Noetherian prime rings, Canad. J. Math. 27 (1975), 867-883. MR 0389958 (52:10787)
  • [18] B. Stenstrōm, An introduction to methods of ring theory, Grundlehren Math. Wiss., Bd. 217, Springer-Verlag, Berlin and New York, 1975.
  • [19] A. A. Tuganbaev, Quasiprojective modules, Sibirsk Mat. Z. (3) 21 (1980), 177-183, 238. MR 574972 (81h:16036)
  • [20] L. E. T. Wu and J. P. Jans, On quasi-projectives, Illinois J. Math. 11 (1967), 439-448. MR 0220765 (36:3817)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1983-0697063-X
Article copyright: © Copyright 1983 American Mathematical Society

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