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The dual notion of prime submodules. (English) Zbl 1090.13005
Summary: In this paper the concept of the second submodule (the dual notion of prime submodule) is introduced. We show that for a finitely cogenerated (the dual notion of finitely generated) module, every non-zero submodule contains a second submodule. It is shown that, if $$M$$ is a finitely generated $$R$$-module and if $$M$$ is a second submodule of itself then the zero submodule of $$M$$ is a prime submodule. Also the dual of this result (in some sense) is shown.

##### MSC:
 13C13 Other special types of modules and ideals in commutative rings 13C11 Injective and flat modules and ideals in commutative rings
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