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.
Ashkan Nikseresht and Abdulrasool Azizi
Shiraz University, Shiraz University
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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