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Some aspects of relative injectivity

Published online by Cambridge University Press:  17 April 2009

S. Feigelstock  and
R. Raphael
S. Feigelstock
Affiliation:
Department of Mathematic, Bar Ilan University, Ramat Gan, Israel.
R. Raphael
Affiliation:
Department of Mathematics, Concordia University, Loyola Campus, 7141 Sherbrooke St. West, Montreal, Quebec H4B 1R6Canada.
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Abstract

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If H and M are right R-modules, H is M-injective if every R-homonorphism N → H, N a right R-submodule of M, can be extended to an R-homonorphism from M to H.

H is strongly M-injective if H is injective for inclusions whose cokernels are isomorphic to factor modules of M.

For the case of abelian groups H and M, one settles the questions “when is H M-injective” and “when is H strongly M-injective”. The latter can be characterized in terms of the vanishing of Ext. Results for general module categories are also given.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 36 , Issue 1 , August 1987 , pp. 161 - 170
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Azumaya, G., Mbuntum, F., Varadarajan, K., “On M-projective and M-injective modules”, Pacific J. Math. 59 (1975), 9–16.Google Scholar
[2]Feigelstock, S. and Raphael, R., “Some aspects of relative projectivity”, Comm. Algebra 14 (1986), 1187–1212.CrossRefGoogle Scholar
[3]Fuchs, L., Abelian groups, Volume 1 (Academic Press, New York, London, 1971).Google Scholar
[4]Hu, S.T., Introduction to Homological Algebra (Holden-Day, 1968).Google Scholar