Modules satisfying the weak Nakayama property |
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Authors: | Mahdi Samiei Hosein Fazaeli Moghimi |
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Affiliation: | Department of Mathematics, University of Birjand, P.O. Box 97175-615, Birjand, Iran |
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Abstract: | Let R be a commutative ring with identity. We will say that an R-module M satisfies the weak Nakayama property, if IM=M, where I is an ideal of R, implies that for any x∈M there exists a∈I such that (a−1)x=0. In this paper, we will study modules satisfying the weak Nakayama property. It is proved that if R is a local ring, then R is a Max ring if and only if J(R), the Jacobson radical of R, is T-nilpotent if and only if every R-module satisfies the weak Nakayama property. |
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Keywords: | Weak Nakayama property Primeful module Max ring |
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