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D-anneaux et anneaux F-semi-parfaits

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1146)

Abstract

This paper is divided in two parts. Part I deals with commutative D-rings. It is to be remembered from [6] that a commutative ring A with identity is said to be a D-ring if for every element x of A, there exist elements a ∈ A, e ∈ A such that e2=e, e=ax, x-xe ∈ J, the Jacobson radical of A. These rings are particular pm-rings studied by De Marco Orsatti[9], i.e. ring in which every prime ideal is contained in a unique maximal ideal, and whose maximal spectrum is consequently compact ; various topological and algebraic properties of pm-rings have been given in [5]. The structure of a D-ring as a subdirect product of local rings was given in [6], together with the construction of the so-called canonical D-envelope of a ring which is a D-ring containing A and having a certain universal property. These results are reviewed here in section 1.

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© 1985 Springer-Verlag

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Contessa, M., Lesieur, L. (1985). D-anneaux et anneaux F-semi-parfaits. In: Malliavin, MP. (eds) Séminaire d'Algèbre Paul Dubreil et Marie-Paule Malliavin. Lecture Notes in Mathematics, vol 1146. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074548

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  • DOI: https://doi.org/10.1007/BFb0074548

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  • Print ISBN: 978-3-540-15686-4

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