Carrés cartésiens et anneaux de pseudo-valuation

Marco Fontana

Publications du Département de mathématiques (Lyon) (1980)

  • Volume: 17, Issue: 1, page 57-95
  • ISSN: 0076-1656

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Fontana, Marco. "Carrés cartésiens et anneaux de pseudo-valuation." Publications du Département de mathématiques (Lyon) 17.1 (1980): 57-95. <http://eudml.org/doc/273557>.

@article{Fontana1980,
author = {Fontana, Marco},
journal = {Publications du Département de mathématiques (Lyon)},
keywords = {overring of pseudo-valuation domain; pull-back; normalisation; ring of fractions},
language = {fre},
number = {1},
pages = {57-95},
publisher = {Université Claude Bernard - Lyon 1},
title = {Carrés cartésiens et anneaux de pseudo-valuation},
url = {http://eudml.org/doc/273557},
volume = {17},
year = {1980},
}

TY - JOUR
AU - Fontana, Marco
TI - Carrés cartésiens et anneaux de pseudo-valuation
JO - Publications du Département de mathématiques (Lyon)
PY - 1980
PB - Université Claude Bernard - Lyon 1
VL - 17
IS - 1
SP - 57
EP - 95
LA - fre
KW - overring of pseudo-valuation domain; pull-back; normalisation; ring of fractions
UR - http://eudml.org/doc/273557
ER -

References

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  1. [1] T. Akiba, A note on AV-domains. Bull. Kyoto Ed. Ser. B31 (1967) , 1-3. Zbl0265.13015MR218339
  2. [2] M.F. Atiyah - I.G. Mac Donald, Introduction to commutative algebra. Addison-Wesley, New York1969. Zbl0175.03601MR242802
  3. [3] D.F. Anderson - D.E. Dobbs, Pair of rings with the same prime ideals. Can. J. Math. (A paraître). Zbl0406.13001MR571931
  4. [4] V. Barucci - M. Fontana, When are D + M rings Laskerian? (A paraître). Zbl0492.13002
  5. [5] E. Bastida - R.W. Gilmer, Overrings and divisoria ! ideals of rings of the form D+M. Michigan Math. J.20 (1974), 79-95. Zbl0239.13001MR323782
  6. [6] N. Bourbaki, Algebre commutative. Ch. 1-7. Hermann, Paris1961/1965. 
  7. [7] J.W. Brewer - R.W. Gilmer, Integral domains whose overrings are ideal transforms. Math. Nach.51 (1971), 255-267. Zbl0203.34602MR309925
  8. [8] D.E. Dobbs, Divided rings and going-down. Pac. J. Math.67 (1976), 353-363. Zbl0326.13002MR424795
  9. [9] D.E. Dobbs, On the weak global dimension of pseudo-valuation domains. Can. Math. Bull. 21 (1978) , 159-164. Zbl0383.13001MR485832
  10. [10] D.E. Dobbs, Coherence, ascent of going-down and pseudo-valuation domains. Houston J. Math.4 (1978), 551-567. Zbl0388.13002MR523613
  11. [11] D.E. Dobbs - M. Fontana - I.J. Papick, On the flat spectral topology and certain distinguished spectral sets. (A paraître). Zbl0483.14001
  12. [12] D.E. Dobbs - I.J. Papick, When is D+M coherent ?Proc. AMS65 (1977), 370-371. Zbl0369.13004MR441948
  13. [13] M. Fontana, Topologically defined classes of commutative rings. Ann. Mat. Pura Appl.123 (1980), 331-355. Zbl0443.13001MR581935
  14. [14] M. Fontana, Carrés cartésiens, anneaux divisés et anneaux localement divisés. Pre-Publ. Math. Univ. Paris-Nord (A paraître). Zbl0475.13008
  15. [15] M. Fontana - P. Maroscia, Sur les anneaux de Goldman. Boll. Un. Mat. Ital.13-B (1976), 743-759. Zbl0351.13002MR463154
  16. [16] R.W. Gilmer, A class of domains in which primary ideals are valuation ideals. Math. Ann.161 (1965), 247-254. Zbl0135.08001MR186689
  17. [17] R.W. Gilmer, A class of domains in which primary ideals are valuation ideals, II. Math. Ann.171 (1967), 93-96. Zbl0146.26301MR215821
  18. [18] R.W. Gilmer, Multiplicative ideal theory. Queen's Math. Papers, Kingston 1968. Rev. Ed. Dekker, New York1972. Zbl0804.13001MR427289
  19. [19] R.W. Gilmer - W. Heinzer, Intersections of quotient rings of an integral domain. J. Math. Kyoto Univ.7 (1967), 133-150. Zbl0166.30601MR223349
  20. [20] R.W. Gilmer - W. Heinzer, Primary ideals and valuation ideals, II. Trans. AMS131 (1968), 149-162. Zbl0169.36401MR220715
  21. [21] R.W. Gilmer - J.A. Huckaba, Δ -rings. J. Algebra28 (1974), 414-432. Zbl0278.13003MR427308
  22. [22] R.W. Gilmer - J. Ohm, Integral domains with quotient overrings. Math. Ann.153 (1964), 97-103. Zbl0128.26004MR159835
  23. [23] V. Greenberg, Global dimension in cartesian squares. J. Algebra32 (1974), 31-43. Zbl0292.13004MR364233
  24. [24] J.R. Hedstrom - E.G. Houston, Pseudo-valuation domains. J. Math.75 (1978), 137-147. Zbl0368.13002MR485811
  25. [25] J.R. Hedstrom - E.G. Houston, Pseudo-valuation domains, II. Houston J. Math.4 (1978), 199-207. Zbl0416.13014MR485812
  26. [26] W. Heinzer, Quotient overrings of an integral domain. Mathematika17 (1970), 139-148. Zbl0201.37202MR265334
  27. [27] I. Kaplansky, Commutative rings. Allyn-Bacon, Boston 1970. Rev. Ed. Univ. Chicago Press1974. Zbl0296.13001MR345945
  28. [28] T. Kikuchi, Some remarks on S-domains. J. Math.Kyoto Univ.6 (1966), 49-60. Zbl0158.03905MR202751
  29. [29] W. Krull, Beiträge zur Arithmetik kommutativer Integritätsbereiche, II. Math. Z.41 (1936), 665 - 679. Zbl62.1105.02MR1545646JFM62.1105.01
  30. [30] J.-P. Lafon, Algèbre commutative : Langages géométrique et algébrique. Hermann, Paris1977. Zbl0907.13001MR460306
  31. [31] S. McAdam, Two conductor theorems. J. Algebra23 (1972) , 239-240. Zbl0254.13009MR304371
  32. [32] P. Maroscia, Topological properties of some classes of G-domains. Boll. Un. Mat. Ital.15-A (1978), Zbl0396.13019MR521116
  33. [33] M. Nagata, Local rings. Interscience, New York1962. Zbl0123.03402MR155856
  34. [34] I.J. Papick, Topologically defined classes of commutative rings. Trans. AMS219 (1976), 1-37. Zbl0345.13005MR401745
  35. [35] I.J. Papick, Finite type extensions and coherence. Pac. J. Math.78 (1978), 161-172. Zbl0363.13010MR513292
  36. [36] I.J. Papick, When coherent pairs are Noetherian pairs. Houston J. Math. (A paraître). Zbl0413.13001MR567912
  37. [37] G. Picavet, Sur les anneaux commutatifs dont tout idéal premier est de Goldman. C.R. Acad. Sc. Paris A 280 (1975), A 1719 - A 1721. Zbl0328.13001MR469900
  38. [38] R. Ramaswamy - T.M Viswanathan, Overring properties of G-domains. Proc. AMS58 (1976) , 59-66. Zbl0323.13003MR407005
  39. [39] P. Ribenboim, Sur une note de Nagata relative à un problème de Krull. Math. Z.64 (1956), 159-168. Zbl0067.26801MR76746
  40. [40] F. Richman, Generalized quotient rings. Proc. AMS16 (1965), 794-799. Zbl0145.27406MR181653
  41. [41] P.B. Sheldon, Prime ideals in GCD-domains. Can. J. Math.26 (1974), 98-107. Zbl0247.13009MR330133
  42. [42] C. Traverso, Seminormality and Picard groupAnn. Sc. Norm. Sup. Pisa24 (1970), 585-595. Zbl0205.50501MR277542
  43. [43] A.R. Wadsworth, Pairs of domains where all intermediate domains are Noetherian. Trans. AMS195 (1974), 201-211. Zbl0294.13010MR349665

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