Geodesic
ON GENERALIZATION OF NAKAYAMA'S LEMMA
Glasgow mathematical journal, Tome 52 (2010) no. 3, pp. 605-617

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DOI

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).
DOI : 10.1017/S0017089510000467
Mots-clés : 13C99, 13C13, 13E05, 13F05, 13F15 
AZIZI, A. ON GENERALIZATION OF NAKAYAMA'S LEMMA. Glasgow mathematical journal, Tome 52 (2010) no. 3, pp. 605-617. doi: 10.1017/S0017089510000467
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