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Our main aim in this note, is a further generalization of a result due to D. D. Anderson, i.e., it is shown that if R is a commutative ring, and M a multiplication R-module, such that every prime ideal minimal over Ann (M) is finitely generated, then M contains only a finite number of minimal prime submodules. This immediately yields that if P is a projective ideal of R, such that every prime ideal minimal over Ann (P) is finitely generated, then P is finitely generated. Furthermore, it is established that if M is a multiplication R-module in which every minimal prime submodule is finitely generated, then R contains only a finite number of prime ideals minimal over Ann (M). © 2007 Springer Science + Business Media B.V.

Original publication

DOI

10.1007/s10474-007-6136-0

Type

Journal article

Journal

Acta mathematica hungarica

Publication Date

01/01/2008

Volume

118

Pages

1 - 7