On quasiprojective covers
HTML articles powered by AMS MathViewer
- by Theodore G. Faticoni PDF
- Trans. Amer. Math. Soc. 278 (1983), 101-113 Request permission
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.References
- Frank W. Anderson and Kent R. Fuller, Rings and categories of modules, Graduate Texts in Mathematics, Vol. 13, Springer-Verlag, New York-Heidelberg, 1974. MR 0417223
- David M. Arnold, Finite rank torsion free abelian groups and rings, Lecture Notes in Mathematics, vol. 931, Springer-Verlag, Berlin-New York, 1982. MR 665251
- D. Arnold, R. S. Pierce, J. D. Reid, C. Vinsonhaler, and W. Wickless, Torsion-free abelian groups of finite rank projective as modules over their endomorphism rings, J. Algebra 71 (1981), no. 1, 1–10. MR 627421, DOI 10.1016/0021-8693(81)90102-2 M. F. Atiyah and I. G. McDonald, Introduction to commutative algebra, Addison-Wesley, Reading, Mass., 1979.
- Hyman Bass, Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960), 466–488. MR 157984, DOI 10.1090/S0002-9947-1960-0157984-8
- A. W. Chatters and C. R. Hajarnavis, Rings with chain conditions, Research Notes in Mathematics, vol. 44, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1980. MR 590045
- David Eisenbud and J. C. Robson, Modules over Dedekind prime rings, J. Algebra 16 (1970), 67–85. MR 289559, DOI 10.1016/0021-8693(70)90041-4 T. G. Faticoni, On classifying quasi-projective modules, Finitely faithful modules and finitely generated quasi-projective modules, Comm. Algebra (submitted).
- K. R. Fuller and D. A. Hill, On quasi-projective modules via relative projectivity, Arch. Math. (Basel) 21 (1970), 369–373. MR 272815, DOI 10.1007/BF01220931
- Joachim Lambek, Lectures on rings and modules, Blaisdell Publishing Co. [Ginn and Co.], Waltham, Mass.-Toronto, Ont.-London, 1966. With an appendix by Ian G. Connell. MR 0206032 K. M. Rangaswamy, Some remarks on the endomorphism rings of quasi-projective modules (to appear).
- K. M. Rangaswamy and N. Vanaja, Quasi projectives in abelian and module categories, Pacific J. Math. 43 (1972), 221–238. MR 314936
- I. Reiner, Maximal orders, London Mathematical Society Monographs, No. 5, Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York, 1975. MR 0393100
- Klaus W. Roggenkamp and Verena Huber-Dyson, Lattices over orders. I, Lecture Notes in Mathematics, Vol. 115, Springer-Verlag, Berlin-New York, 1970. MR 0283013
- Klaus W. Roggenkamp and Verena Huber-Dyson, Lattices over orders. I, Lecture Notes in Mathematics, Vol. 115, Springer-Verlag, Berlin-New York, 1970. MR 0283013
- Surjeet Singh, Quasi-injective and quasi-projective modules over hereditary Noetherian prime rings, Canadian J. Math. 26 (1974), 1173–1185. MR 352175, DOI 10.4153/CJM-1974-110-5
- Surjeet Singh, Modules over hereditary Noetherian prime rings, Canadian J. Math. 27 (1975), no. 4, 867–883. MR 389958, DOI 10.4153/CJM-1975-094-3 B. Stenstrōm, An introduction to methods of ring theory, Grundlehren Math. Wiss., Bd. 217, Springer-Verlag, Berlin and New York, 1975.
- A. A. Tuganbaev, Quasiprojective modules, Sibirsk. Mat. Zh. 21 (1980), no. 3, 177–183, 238 (Russian). MR 574972
- L. E. T. Wu and J. P. Jans, On quasi projectives, Illinois J. Math. 11 (1967), 439–448. MR 220765
Additional Information
- © Copyright 1983 American Mathematical Society
- 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