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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Bibliographie
K. AOYAMA, On the structure space of a direct product of a ring, J. Sc. Hiroshima Univ., 34 (1970), 339–353.
H. BASS, Finitistic Dimension and a homological generalization of semiprimary rings, Trans. Amer. Math. Soc. 95 (1960), 446–488.
R. BKOUCHE, Couples spectraux et faisceaux associés. Applications aux anneaux de fonctions (thèse). Bull. Soc. Math. France, 98 (1970), 253–295.
A.H. CLIFFORD and G.B. PRESTON, The Algebraic Theory of Semi-groups, Vol. I, Mathematical Surveys, 1961.
M. CONTESSA, On pm-rings, Comm. Alg., 10 (1982), 93–108.
M. CONTESSA, On certain classes of pm-rings, (To appear in Comm. Alg. 1984).
M. CONTESSA, D-enveloppe d'un domaine. Cas de l'anneau ℂ[x1,...,Xn], Comptes-rendus du 108e Congrès National des Sociétés savantes, Sciences, Grenoble, 1983.
P.M. COHN, Free Rings and their Relations, Academic Press, 1971.
G. DE MARCO-A. ORSATTI, Commutative rings in which every prime ideal is contained in a unique maximal ideal, Proc. Amer. Math. Soc., 30 (1971), 459–466.
J.M. GOURSAULT, Sur les anneaux introduits par la notion de module projectif, (Thèse de Doctorat, Poitiers, 1977).
N. JACOBSON, Structure of Rings, Amer. Math. Soc. Coll. Publications, Volumme XXXVII, (1964).
I. KAPLANSKY, Rings of Operators, W.A. Benjamin, Inc., 1968.
G.S. MONK, A characterization of exchange Rings, Proc. Amer. Math. Soc., 35, 2, (1972), 349–353.
U. OBERST und H.J. SCHNEIDER, Die Struktur von projektiven Moduln, Inventiones math., 13 (1971), 295–304.
G. RENAULT, Algèbre non commutative, Paris Gauthier-Villars (1975).
G. RENAULT, Sur les anneaux A tels que tout A-module non nul contient un idéal maximal, C.R. Acad. Sci. Paris, 264, (1967), 622–624.
J. VALETTE, Anneaux de groupes et actions de groupes. (Thèse de Doctorat, Poitiers, 1983).
R.B. WARFIELD Jr., Exchange Rings and Decompositions of Modules Math. Ann. 199 (1972), 31–36.
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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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