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Vietnam Journal of Mathematics 38:1 (2010) 55-62  

On Arithmetical Rings and the Radical Formula

A. Nikseresht and A. Azizi

Abstract.  In this paper we investigate the radical formula in modules over arithmetical rings. Particularly we prove that every module over a finite dimensional arithmetical ring and every Prüfer module over an arbitrary arithmetical ring satisfies the radical formula. Also we give a necessary and sufficient condition for a serial module to satisfy the radical formula.

2000 Mathematics Subject Classification: 13C99, 13A15, 13F05, 13C13.

Keywords: Prime submodule, radical formula, arithmetical ring, invertible submodule.

 

 

 

 

 

 

 

 

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