ACTA MATHEMATICA UNIVERSITATIS COMENIANAE
Vol. LXXVI, 2 (2007)
p. 179 - 188
Some Comments on Injectivity and p-injectivity
R. Yue Chi Ming
Abstract.
A generalization of injective modules (noted GI-modules), distinct from
p-injective modules, is introduced. Rings whose p-injective modules are GI are characterized.
If M is a left GI-module, E = End (AM), then
E/J(E) is von Neumann regular, where J(E) is the
Jacobson radical of the ring E. A is semi-simple Artinian if, and only if, every left A-module
is GI. If A is a left p. p., left GI-ring such that every non-zero complement left ideal of A
contains a non-zero ideal of A, then A is strongly regular. Sufficient conditions are given for a
ring to be either von Neumann regular or quasi-Frobenius. Quasi-Frobenius and von
Neumann regular rings are characterized. Kasch rings are also considered.
Keywords:
injective; GI-module; p-injective; YJ-injective;
von Neumann regular; quasi-Frobenius ring.
AMS Subject classification. Primary:16D40, 16D50, 16E50 16D40, 16D50, 16E50.
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