Bibliographie
D. F. Anderson andD. E. Dobbs, Pairs of rings with the same prime ideals. Canadian J. Math.32, 362–384 (1980).
T. Arnold andR. Gilmer, Dimension sequences for commutative rings. Bull. Amer. Math. Soc.79, 407–409 (1973).
E. Bastida andR. Gilmer, Overrings and divisorial ideals of rings of the formD+M. Michigan Math. J.209, 79–95 (1973).
M. B. Boisen andP. B. Sheldon,CPI-extensions: overrings of integral domains with special spectrum. Canadian J. Math.29, 722–737 (1977).
J. W. Brewer, P. A. Montgomery, P. A. Rutter andW. J. Heinzer, Krull dimension of polynomial rings. LNM311, 26–46, Berlin-Heidelberg-New York 1973.
J. W. Brewer andE. A. Rutter,D+M constructions with general overrings. Michigan J.23, 33–42 (1976).
P.-J. Cahen andY. Haouat, Spectra d'anneaux de polynômes sur une suite croissante d'anneaux. Arch. Math.49, 281–285 (1987).
D. Costa, J. Mott andM. Zafrullah, The constructionD+XD s [X]. J. Algebra53, 423–439 (1978).
P. M. Eakin, The converse of a wellknown theorem on Noetherian rings. Math. Ann.177, 278–282 (1968).
M. Fontana, Topologically defined classes of commutative rings. Ann. Mat. Bura Appl.123, 331–355 (1980).
M.Fontana, Carrés cartésiens, anneaux divisés et anneaux localement divisés. Prépublication de l'Univ. de Paris-Nord21 (1980).
R.Gilmer, Multiplicative ideal theory. New York 1972.
R. Gilmer, Two constructions of Prüfer domains. J. Reine Angew. Math.239–240, 153–162 (1962).
Y. Haouat, Spectre d'anneaux à plusieurs variables sur une suite croissante d'anneaux. Arch. Math.50, 236–240 (1988).
J. R. Hedstrom andE. G. Houston, Pseudo-valuation domains. Pacific. J. Math.75, 137–147 (1978).
J. R. Hedstrom andE. G. Houston, Pseudo-valuation domains II Houston J. Math.4, 199–207 (1978).
P.Jaffard, Théorie de la dimension des anneaux de polynômes. Paris 1960.
M.Nagata, Local rings. New York 1975.
T. Parker, A number theoretic characterization of dimension sequences. Amer. J. Math.97, 308–311 (1975).
A. Seidenberg, A note on the dimension of rings. Pacific J. Math.3, 505–512 (1953).
A. Seidenberg, A note on the dimension of rings II. Pacific J. Math.4, 603–614 (1954).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Cahen, P.J. Couples d'anneaux partageant un idéal. Arch. Math 51, 505–514 (1988). https://doi.org/10.1007/BF01261971
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01261971