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ON GENERALIZATION OF NAKAYAMA'S LEMMA

Published online by Cambridge University Press:  25 August 2010

A. AZIZI
A. AZIZI*
Affiliation:
Department of Mathematics, College of Sciences, Shiraz University, Shiraz 71457-44776, Iran e-mail: aazizi@shirazu.ac.ir
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Abstract

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Let R be a commutative ring with identity. We will say that an R-module M has Nakayama property, if IM = M, where I is an ideal of R, implies that there exists a ∈ R such that aM = 0 and a − 1 ∈ I. Nakayama's Lemma is a well-known result, which states that every finitely generated R-module has Nakayama property. In this paper, we will study Nakayama property for modules. It is proved that R is a perfect ring if and only if every R-module has Nakayama property (Theorem 4.9).

Keywords

13C9913C1313E0513F0513F15
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 3 , September 2010 , pp. 605 - 617
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

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