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MODULES WHICH ARE SUBISOMORPHIC TO QUASI-INJECTIVE MODULES | ||
| Iraqi Journal of Science | ||
| Article 1, Volume 50, Issue 2, 2009, Pages 226-230 | ||
| Author | ||
| Amer H. H. Al-Khaladi | ||
| Abstract | ||
| Let be a commutative ring with identity and let be a unitary left module. We call the module kerquasi-injective if for every monomorphism from into , where is a submodule of and is a quasi-injective hull of and for every homomorphism from into , there exists a homomorphism from into such that .It is clear that every quasi-injective module is kerquasi-injective, however the converse is false. Also every ker-injective module is kerquasi-injective, however the converse is false. In this paper we give some characterizations of kerquasi-injective modules, we also study some conditions under which a kerqausi-injective module becomes quasi-injective. For example, if a kerquasi-injective module is a finitely generated, then it is a quasi-injective. We ought to mention that we were not able to give an example of a kerquasi-injective module which is not quasi-injective and ker-injective. | ||
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