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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.

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