Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-24T23:14:48.206Z Has data issue: false hasContentIssue false
  • English
  • Français

Restricted homological properties of modules

Published online by Cambridge University Press:  09 April 2009

David A. Hill
David A. Hill
Affiliation:
Department of Mathematics, University of Western Australia.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let R be a ring and M a left R-module. We investigate when the functors HomR(M, —), HomR( —, M), and — ⊗RM are exact for certain restricted subcategories of modules.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 18 , Issue 2 , September 1974 , pp. 170 - 181
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Anderson, F. W., Structure of rings and algebras (Lecture Notes, University of Oregon, 1966–1967).Google Scholar
[2]Bass, H., ‘Finistric dimension and a homological generalization of semi-primary rings’, Trans. Amer. Math. Soc. 95 (1960), 466–488.CrossRefGoogle Scholar
[3]Bourbaki, N., Algèbre Commutative, Chapters I–II (Act. Sc. Ind. 1290, Paris: Hermann, 1961).Google Scholar
[4]Chase, S., ‘Direct products of modules’, Trans. Amer. Math. Soc. 95 (1960), 457–473.CrossRefGoogle Scholar
[5]Curtis, C. W. and Reiner, I., Representation Theory of Finite Groups and Associative Algebras (New York: Interscience, 1962).Google Scholar
[6]Eckman, B. and Schopf, A., ‘Über injecktive Moduln’, Arch. Math. 4 (1953), 75–78.CrossRefGoogle Scholar
[7]Faith, C., ‘Rings with ascending condition on annihilators’, Nagoya Math. J. 27 (1966), 179–191.CrossRefGoogle Scholar
[8]Faith, C. and Utumi, Y., ‘Quasi-injective modules and their endomorphism rings’, Arch. Math. 15 (1964), 166–174.CrossRefGoogle Scholar
[9]Faith, K. and Walker, E. A., ‘Direct-sum representations of injective modules’, J. Algebra 5 (1967), 203–221.CrossRefGoogle Scholar
[10]Fuller, K. R., ‘On direct representations of quasi-injectives and quasi projectives’, Arch. Math. 20 (1969), 495–502.CrossRefGoogle Scholar
[11]Fuller, K. R., ‘Relative projectivity and injectivity classes determined by Simple Modules’, (To appear).Google Scholar
[12]Fuller, K. R. and Hill, D. A., ‘On quasi-projective modules via relative projectivity’, (To appear).Google Scholar
[13]Golan, J. S., ‘Characterizations of rings using quasi-projective modules’, Israel J. Math. 8 (1970), 34–38.CrossRefGoogle Scholar
[14]Govorov, V. E., ‘Rings over which flat modules are free’, Soviet Math. 3 (1962), 836–838.Google Scholar
[15]Harada, M., ‘Note on quasi-injective modules’, Osaka J. Math. 2 (1965), 351–356.Google Scholar
[16]Jacobson, N., Structure of Rings, Rev. Ed. (Providence, 1964).Google Scholar
[17]Jans, J. P., ‘Projective injective modules’, Pacificx J. Math. 9 (1959), 1103–1108.CrossRefGoogle Scholar
[18]Jans, J. P., Rings and Homology (New York: Holt, Rinehart, and Winston, 1964).Google Scholar
[19]Jans, J. and Wu, L. E. T., ‘On quasi-projectives’, Illinois J. Math. 11 (1967), 439–448.Google Scholar
[20]Johnson, R. E. and Wong, E. T., ‘Quasi-injective modules and irreducible rings’, J. London Math. Soc. 36 (1961), 260–268.CrossRefGoogle Scholar
[21]Koehler, A., ‘Quasi-projective and quasi-injective modules’, (To appear).Google Scholar
[22]Koehler, A., ‘Quasi-projective covers and direct sums’, (To appear).Google Scholar
[23]Kurshen, R. P., Injective modules with a finitely generated essential socle (Ph. D. thesis, Notices Amer. Math. Soc., 16 (1969).Google Scholar
[24]Lambek, J., Lectures on Rings and Modules (Waltham, Massachusetts: Blaisdell, 1966).Google Scholar
[25]Lambek, J., ‘A module is flat if and only if its character module is injective’, Canad. Math. Bull. 7 (1963), 237–243.CrossRefGoogle Scholar
[26]Morita, K., ‘On the S-rings in the sense of F. Kasch’, Nagoya Math. J. 27 (1966), 687–695.CrossRefGoogle Scholar
[27]Robert, E., ‘Projectives et injectives relatifs’, C. R. Acad. Sci. Paris Ser. A. B. 286 (1960), Ser. A. 361–364.Google Scholar