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http://dx.doi.org/10.4134/JKMS.2013.50.6.1183

PRIME BASES OF WEAKLY PRIME SUBMODULES AND THE WEAK RADICAL OF SUBMODULES  

Nikseresht, Ashkan (Department of Mathematics College of Sciences Shiraz University)
Azizi, Abdulrasool (Department of Mathematics College of Sciences Shiraz University)
Publication Information
Journal of the Korean Mathematical Society / v.50, no.6, 2013 , pp. 1183-1198 More about this Journal
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;
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