Existence of homomorphism in Modules

Asked Sep 06 '15 at 17:48

Active Sep 06 '15 at 18:16

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I'm studying projective and injective modules and a serious question raised for me: what is the necessary and sufficient conditions for existence of homomorphisms between modules?

I mean non-trivial case.
I know it is very broad question. But at least it might have been categorized to some extent.
Classification is one of the most important things in mathematics so it could be an interesting material for research.

edited Sep 06 '15 at 18:16

asked Sep 06 '15 at 17:48

Mojee KD

1

Well there's always the zero homomorphism ... Little more can be said in general – Hagen von Eitzen Sep 06 '15 at 17:52
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This is far, far too broad. – Matt Samuel Sep 06 '15 at 17:57
Why too broad? It's a reasonable question to ask and we know how to answer it for vector spaces over a field. So what can we say about modules over other rings? – Rob Arthan Sep 06 '15 at 23:22

Existence of homomorphism in Modules

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