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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.

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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