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Vietnam
Journal of Mathematics 38:1 (2010) 55-62
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On Arithmetical Rings and the Radical Formula
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A. Nikseresht and
A. Azizi
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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.
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2000 Mathematics Subject Classification: 13C99, 13A15,
13F05, 13C13.
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Keywords: Prime submodule, radical formula,
arithmetical ring, invertible submodule.
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