Uniformly classical quasi-primary submodules

Naderi, M.H.

Uniformly classical quasi-primary submodules

Document Type : Research Paper

Author

M.H. Naderi

University of Qom

Abstract

In this paper we introduce the notions of uniformly quasi-primary ideals and uniformly classical quasi-primary submodules that generalize the concepts of uniformly primary ideals and uniformly classical primary submodules; respectively. Several characterizations of classical quasi-primary and uniformly classical quasi-primary submodules are given.
Then we investigate for a ring $R$, when any finite intersection of (uniformly) primary submodules of any $R$-module is a (uniformly) classical quasi-primary submodule. Furthermore, the behavior of classical quasi-primary and uniformly classical quasi-primary submodules under localizations are studied. Also, we investigate the existence of (minimal) primary submodules containing classical quasi-primary submodules.

Keywords

References

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