Dimension des couples d'anneaux partageant un idéal

Paul-Jean Cahen

Publications du Département de mathématiques (Lyon) (1988)

  • Volume: 51, Issue: 3B, page 69-75
  • ISSN: 0076-1656

How to cite

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Cahen, Paul-Jean. "Dimension des couples d'anneaux partageant un idéal." Publications du Département de mathématiques (Lyon) 51.3B (1988): 69-75. <http://eudml.org/doc/273555>.

@article{Cahen1988,
author = {Cahen, Paul-Jean},
journal = {Publications du Département de mathématiques (Lyon)},
keywords = {proper couple; valuation ring; construction; shared ideal; Krull dimension; lifting of prime ideals},
language = {fre},
number = {3B},
pages = {69-75},
publisher = {Université Claude Bernard - Lyon 1},
title = {Dimension des couples d'anneaux partageant un idéal},
url = {http://eudml.org/doc/273555},
volume = {51},
year = {1988},
}

TY - JOUR
AU - Cahen, Paul-Jean
TI - Dimension des couples d'anneaux partageant un idéal
JO - Publications du Département de mathématiques (Lyon)
PY - 1988
PB - Université Claude Bernard - Lyon 1
VL - 51
IS - 3B
SP - 69
EP - 75
LA - fre
KW - proper couple; valuation ring; construction; shared ideal; Krull dimension; lifting of prime ideals
UR - http://eudml.org/doc/273555
ER -

References

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  1. [1] Anderson, D.F., Dobbs, D.E. : Pairs of rings with the same prime ideals. Canadian J.of Math.32. 362-384 (1980) Zbl0406.13001MR571931
  2. [2] Bastida, E., Gilmer, R. : Overrings and divisorial ideals of rings of the form D + M. Michigan Math.J.209, 79-95 (1973) Zbl0239.13001MR323782
  3. [3] Boisen, M.B., Sheldon, P.B. : CPI-extensions : overrings of integral domains with special spectrum. Canadian J.of Math.29, 722-737 (1977) Zbl0363.13002MR447205
  4. [4] Brewer, J.W., Montgomery, P.A., Rutter, P.A., Heinzer, W.J. : Krull dimension of polynomial rings. Lecture notes311. 26-46 (1973) Springer Verlag Zbl0249.13004MR337927
  5. [5] Brewer, J.W., Rutter, E.A. : D+M constructions with general overrings ; Michigan J.23, 33-42 (1976) Zbl0318.13007MR401744
  6. [6] Cahen, P.-J. : Couples d'anneaux partageant un idéal. (A paraître). Archiv der Math Zbl0668.13005
  7. [7] Cahen, P.-J. : Dimension des couples d'anneaux partageant un idéal. (A paraître). Archiv der Math Zbl0668.13005
  8. [8] Cahen, P-J., Haouat, Y. : Spectre d'anneaux de polynômes sur une suite croissante d'anneaux. Archiv der Math49, 281-285 (1987) Zbl0601.13006MR913157
  9. [9] Costa, D., Mott, J., Zafrullah, M. : The construction D + X D s [ X ] J.of Algebra53, 423-439 (1978) Zbl0407.13003MR506224
  10. [10] Eakin, P.M. : The converse of a wellknown theorem on Noetherian rings. Math.Ann.177, 278-282 (1968) Zbl0155.07903MR225767
  11. [11] Fontana, M. : Topologically defined classes of commutative ringsAnnali Matematica pura ed applicata123, 331-355 (1980) Zbl0443.13001MR581935
  12. [12] Fontana, M. : Carrés cartésiens, anneaux divisés et anneaux localement divisés. Prépublication de l'Univ. de Paris-Nord N° 21 
  13. [13] Gilmer, R. : Multiplicative ideal theory. Dekker, New-York (1972) Zbl0248.13001MR427289
  14. [14] Haouat, Y. : Spectre d'anneaux à plusieurs variables sur une suite croissante d'anneaux. Archiv der Math.50, 236-240 (1988) Zbl0625.13012MR933917
  15. [15] Hedstrom, J.R., Houston, E.G. : Pseudo-valuation domains. Pacific.J.Math.75, 137-147 (1978) Zbl0368.13002MR485811
  16. [16] Hedstrom, J.R., Houston, E.G. : Pseudo-valuation domains II. Houston J.Math.4, 199-207 (1978) Zbl0416.13014MR485812
  17. [17] Jaffard, P. : Théorie de la dimension des anneaux de polynômes. Gauthiers Villars, Paris (1960) Zbl0083.03202
  18. [18] Nagata, M. : Local rings. R.E. Krieger, New-York (1975) Zbl0386.13010MR460307
  19. [19] Parker, T. : A number theoretic characterization of dimension sequences. Amer .J.Math.97, 308-311 (1975) Zbl0316.13006MR374122
  20. [20] Seidenberg, A. : A note on the dimension of rings. Pacific J.of Math, 3., 505-512 (1953) Zbl0052.26902MR54571
  21. [21] Seidenberg, A. : A note on the dimension of rings II. Pacific J.of Math4, 603-614 (1954) Zbl0057.26802MR65540

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