The dual notion of prime submodules. (English) Zbl 1090.13005

Yassemi, Siamak

Arch. Math., Brno 37, No. 4, 273-278 (2001).

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

Keywords:

prime submodule; second submodule; injective and flat module