Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2013; 50(6): 1183-1198

Printed November 1, 2013

https://doi.org/10.4134/JKMS.2013.50.6.1183

Copyright © The Korean Mathematical Society.

Prime bases of weakly prime submodules and the weak radical of submodules

Ashkan Nikseresht and Abdulrasool Azizi

Shiraz University, Shiraz University

Abstract

We will introduce and study the notion of prime bases for weakly prime submodules and utilize them to derive some formulas on the weak radical of submodules of a module. In particular, we will show that every one dimensional integral domain weakly satisfies the radical formula and state some necessary conditions on local integral domains which are semi-compatible or satisfy the radical formula and also on Noetherian rings which weakly satisfy the radical formula.

Keywords: prime basis of a submodule, weakly prime submodule, prime submodule, radical formula

MSC numbers: Primary 13C99; Secondary 13C13, 13E05

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