Quasi-primary submodules satisfying the primeful property II

Year 2015, Volume: 44 Issue: 4, 801 - 811, 01.08.2015

Hosein Fazaeli Moghimi , Mahdi Samiei

Abstract

In this paper we continue our study about quasi-primary submodules
(probably satisfying the primeful property), that was defined and studied in Part I (see [8]). We define a quasi-primary decomposition for
submodules of a module over a commutative ring with identity and
study various types of the corresponding minimal forms. In particular, we discuss these decompositions for submodules of multiplication
modules and also arbitrary modules over Noetherian rings. 

Keywords

Quasi-primary submodule, Primeful property, Radical of a sub- module, Multiplication module, Reduced quasi-primary decomposition, Module- reduced quasi-primary decomposition, Shortest quasi-primary decomposition

References

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