Carrés cartésiens et anneaux de pseudo-valuation
Publications du Département de mathématiques (Lyon), Tome 17 (1980) no. 1, pp. 57-95.
@article{PDML_1980__17_1_57_0,
     author = {Fontana, Marco},
     title = {Carr\'es cart\'esiens et anneaux de pseudo-valuation},
     journal = {Publications du D\'epartement de math\'ematiques (Lyon)},
     pages = {57--95},
     publisher = {Universit\'e Claude Bernard - Lyon 1},
     volume = {17},
     number = {1},
     year = {1980},
     zbl = {0475.13008},
     language = {fr},
     url = {http://archive.numdam.org/item/PDML_1980__17_1_57_0/}
}
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Fontana, Marco. Carrés cartésiens et anneaux de pseudo-valuation. Publications du Département de mathématiques (Lyon), Tome 17 (1980) no. 1, pp. 57-95. http://archive.numdam.org/item/PDML_1980__17_1_57_0/

[1] T. Akiba, A note on AV-domains. Bull. Kyoto Ed. Ser. B 31 (1967) , 1-3. | MR 218339 | Zbl 0265.13015

[2] M.F. Atiyah - I.G. Mac Donald, Introduction to commutative algebra. Addison-Wesley, New York 1969. | MR 242802 | Zbl 0175.03601

[3] D.F. Anderson - D.E. Dobbs, Pair of rings with the same prime ideals. Can. J. Math. (A paraître). | MR 571931 | Zbl 0406.13001

[4] V. Barucci - M. Fontana, When are D + M rings Laskerian? (A paraître). | Zbl 0492.13002

[5] E. Bastida - R.W. Gilmer, Overrings and divisoria ! ideals of rings of the form D+M. Michigan Math. J. 20 (1974), 79-95. | MR 323782 | Zbl 0239.13001

[6] N. Bourbaki, Algebre commutative. Ch. 1-7. Hermann, Paris 1961/1965.

[7] J.W. Brewer - R.W. Gilmer, Integral domains whose overrings are ideal transforms. Math. Nach. 51 (1971), 255-267. | MR 309925 | Zbl 0203.34602

[8] D.E. Dobbs, Divided rings and going-down. Pac. J. Math. 67 (1976), 353-363. | MR 424795 | Zbl 0326.13002

[9] D.E. Dobbs, On the weak global dimension of pseudo-valuation domains. Can. Math. Bull. 21 (1978) , 159-164. | MR 485832 | Zbl 0383.13001

[10] D.E. Dobbs, Coherence, ascent of going-down and pseudo-valuation domains. Houston J. Math. 4 (1978), 551-567. | MR 523613 | Zbl 0388.13002

[11] D.E. Dobbs - M. Fontana - I.J. Papick, On the flat spectral topology and certain distinguished spectral sets. (A paraître). | Zbl 0483.14001

[12] D.E. Dobbs - I.J. Papick, When is D+M coherent ? Proc. AMS 65 (1977), 370-371. | MR 441948 | Zbl 0369.13004

[13] M. Fontana, Topologically defined classes of commutative rings. Ann. Mat. Pura Appl. 123 (1980), 331-355. | MR 581935 | Zbl 0443.13001

[14] M. Fontana, Carrés cartésiens, anneaux divisés et anneaux localement divisés. Pre-Publ. Math. Univ. Paris-Nord (A paraître).

[15] M. Fontana - P. Maroscia, Sur les anneaux de Goldman. Boll. Un. Mat. Ital. 13-B (1976), 743-759. | MR 463154 | Zbl 0351.13002

[16] R.W. Gilmer, A class of domains in which primary ideals are valuation ideals. Math. Ann. 161 (1965), 247-254. | MR 186689 | Zbl 0135.08001

[17] R.W. Gilmer, A class of domains in which primary ideals are valuation ideals, II. Math. Ann. 171 (1967), 93-96. | MR 215821 | Zbl 0146.26301

[18] R.W. Gilmer, Multiplicative ideal theory. Queen's Math. Papers, Kingston 1968. Rev. Ed. Dekker, New York 1972. | MR 427289 | Zbl 0804.13001

[19] R.W. Gilmer - W. Heinzer, Intersections of quotient rings of an integral domain. J. Math. Kyoto Univ. 7 (1967), 133-150. | MR 223349 | Zbl 0166.30601

[20] R.W. Gilmer - W. Heinzer, Primary ideals and valuation ideals, II. Trans. AMS 131 (1968), 149-162. | MR 220715 | Zbl 0169.36401

[21] R.W. Gilmer - J.A. Huckaba, Δ-rings. J. Algebra 28 (1974), 414-432. | MR 427308 | Zbl 0278.13003

[22] R.W. Gilmer - J. Ohm, Integral domains with quotient overrings. Math. Ann. 153 (1964), 97-103. | MR 159835 | Zbl 0128.26004

[23] V. Greenberg, Global dimension in cartesian squares. J. Algebra 32 (1974), 31-43. | MR 364233 | Zbl 0292.13004

[24] J.R. Hedstrom - E.G. Houston, Pseudo-valuation domains. J. Math. 75 (1978), 137-147. | MR 485811 | Zbl 0368.13002

[25] J.R. Hedstrom - E.G. Houston, Pseudo-valuation domains, II. Houston J. Math. 4 (1978), 199-207. | MR 485812 | Zbl 0416.13014

[26] W. Heinzer, Quotient overrings of an integral domain. Mathematika 17 (1970), 139-148. | MR 265334 | Zbl 0201.37202

[27] I. Kaplansky, Commutative rings. Allyn-Bacon, Boston 1970. Rev. Ed. Univ. Chicago Press 1974. | MR 345945 | Zbl 0296.13001

[28] T. Kikuchi, Some remarks on S-domains. J. Math. Kyoto Univ. 6 (1966), 49-60. | MR 202751 | Zbl 0158.03905

[29] W. Krull, Beiträge zur Arithmetik kommutativer Integritätsbereiche, II. Math. Z. 41 (1936), 665 - 679. | JFM 62.1105.01 | MR 1545646

[30] J.-P. Lafon, Algèbre commutative : Langages géométrique et algébrique. Hermann, Paris 1977. | MR 460306 | Zbl 0907.13001

[31] S. Mcadam, Two conductor theorems. J. Algebra 23 (1972) , 239-240. | MR 304371 | Zbl 0254.13009

[32] P. Maroscia, Topological properties of some classes of G-domains. Boll. Un. Mat. Ital. 15-A (1978), | MR 521116 | Zbl 0396.13019

[33] M. Nagata, Local rings. Interscience, New York 1962. | MR 155856 | Zbl 0123.03402

[34] I.J. Papick, Topologically defined classes of commutative rings. Trans. AMS 219 (1976), 1-37. | MR 401745 | Zbl 0345.13005

[35] I.J. Papick, Finite type extensions and coherence. Pac. J. Math. 78 (1978), 161-172. | MR 513292 | Zbl 0363.13010

[36] I.J. Papick, When coherent pairs are Noetherian pairs. Houston J. Math. (A paraître). | MR 567912 | Zbl 0413.13001

[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. | MR 469900 | Zbl 0328.13001

[38] R. Ramaswamy - T.M Viswanathan, Overring properties of G-domains. Proc. AMS 58 (1976) , 59-66. | MR 407005 | Zbl 0323.13003

[39] P. Ribenboim, Sur une note de Nagata relative à un problème de Krull. Math. Z. 64 (1956), 159-168. | MR 76746 | Zbl 0067.26801

[40] F. Richman, Generalized quotient rings. Proc. AMS 16 (1965), 794-799. | MR 181653 | Zbl 0145.27406

[41] P.B. Sheldon, Prime ideals in GCD-domains. Can. J. Math. 26 (1974), 98-107. | MR 330133 | Zbl 0247.13009

[42] C. Traverso, Seminormality and Picard group Ann. Sc. Norm. Sup. Pisa 24 (1970), 585-595. | Numdam | MR 277542 | Zbl 0205.50501

[43] A.R. Wadsworth, Pairs of domains where all intermediate domains are Noetherian. Trans. AMS 195 (1974), 201-211. | MR 349665 | Zbl 0294.13010