Bouchiba, S. and El-Arabi, M. (2019) On property (A) for modules over direct products of rings. Quaestiones Mathematicae.

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Abstract

In this paper we show that if Rii∈I is a family of commutative rings and Mii∈I is a family of modules such that each Mi is an Ri-module, then the direct product (Figure presented.) Mi is a (Figure presented.) -module over (Figure presented.) Ri if and only if each Mi is an (Figure presented.) -module over Ri, i ∈ I. This result extends the work of Hong, Kim, Lee and Ryu in Rings with Property ((Figure presented.)) and their extensions, J. Algebra315 (2007), 612–628. Moreover, we characterize Property ((Figure presented.)) for modules in terms of Property ((Figure presented.)) of their total quotient modules, extending the work of Dobbs and Shapiro in On the strong ((Figure presented.))-ring of Mahdou and Hassani, Mediterr. J. Math.10 (2013), 1995–1997. © 2019, © 2019 NISC (Pty) Ltd.

Item Type: Article
Subjects: Mathematics
Divisions: SCIENTIFIC PRODUCTION > Mathematics
Depositing User: Administrateur Eprints Administrateur Eprints
Last Modified: 31 Jan 2020 15:48
URI: http://eprints.umi.ac.ma/id/eprint/3869

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