×

Topologically defined classes of going-down domains. (English) Zbl 0345.13005


MSC:

14E22 Ramification problems in algebraic geometry
13G05 Integral domains
13J99 Topological rings and modules
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Eduardo Bastida and Robert Gilmer, Overrings and divisorial ideals of rings of the form \?+\?, Michigan Math. J. 20 (1973), 79 – 95. · Zbl 0239.13001
[2] N. Bourbaki, Commutative algebra, Addison-Wesley, Reading, Mass., 1972.
[3] Jeffrey Dawson and David E. Dobbs, On going down in polynomial rings, Canad. J. Math. 26 (1974), 177 – 184. · Zbl 0242.13015 · doi:10.4153/CJM-1974-017-9
[4] David E. Dobbs, On going down for simple overrings, Proc. Amer. Math. Soc. 39 (1973), 515 – 519. · Zbl 0238.13019
[5] David E. Dobbs, On going down for simple overrings. II, Comm. Algebra 1 (1974), 439 – 458. · Zbl 0285.13001 · doi:10.1080/00927877408548715
[6] David E. Dobbs and Ira J. Papick, On going-down for simple overrings. III, Proc. Amer. Math. Soc. 54 (1976), 35 – 38. · Zbl 0285.13002
[7] D. E. Dobbs, Ascent and descent of going-down rings for integral extensions (submitted). · Zbl 0327.13007
[8] James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass., 1966. · Zbl 0144.21501
[9] D. Ferrand, Morphismes entiers universellement ouverts (manuscript).
[10] Robert Gilmer and William J. Heinzer, Intersections of quotient rings of an integral domain, J. Math. Kyoto Univ. 7 (1967), 133 – 150. · Zbl 0166.30601
[11] Robert W. Gilmer, Multiplicative ideal theory, Queen’s Papers in Pure and Applied Mathematics, No. 12, Queen’s University, Kingston, Ont., 1968. · Zbl 0155.36402
[12] Robert W. Gilmer Jr., The pseudo-radical of a commutative ring, Pacific J. Math. 19 (1966), 275 – 284. · Zbl 0147.01501
[13] Robert Gilmer, Prüfer-like conditions on the set of overrings of an integral domain, Conference on Commutative Algebra (Univ. Kansas, Lawrence, Kan., 1972), Springer, Berlin, 1973, pp. 90 – 102. Lecture Notes in Math., Vol. 311.
[14] Robert Gilmer and James A. Huckaba, \?-rings, J. Algebra 28 (1974), 414 – 432. · Zbl 0278.13003 · doi:10.1016/0021-8693(74)90050-7
[15] B. Greenberg, Ph.D. Dissertation, Rutgers University, New Brunswick, N. J., 1973.
[16] F. Bombal, Alexander Grothendieck’s work on functional analysis, Advanced courses of mathematical analysis. II, World Sci. Publ., Hackensack, NJ, 2007, pp. 16 – 36. · Zbl 1149.46001 · doi:10.1142/9789812708441_0002
[17] M. Hochster, Non-openness of loci in Noetherian rings, Duke Math. J. 40 (1973), 215 – 219. · Zbl 0257.13015
[18] Irving Kaplansky, Commutative rings, Allyn and Bacon, Inc., Boston, Mass., 1970. · Zbl 0238.16001
[19] -, Topics in commutative ring theory, University of Chicago, Chicago, Ill. (mimeographed notes). · Zbl 0348.13001
[20] William J. Lewis, The spectrum of a ring as a partially ordered set, J. Algebra 25 (1973), 419 – 434. · Zbl 0266.13010 · doi:10.1016/0021-8693(73)90091-4
[21] William S. Massey, Algebraic topology: An introduction, Harcourt, Brace & World, Inc., New York, 1967. · Zbl 0153.24901
[22] Hideyuki Matsumura, Commutative algebra, W. A. Benjamin, Inc., New York, 1970. · Zbl 0441.13001
[23] Stephen McAdam, Going down in polynomial rings, Canad. J. Math. 23 (1971), 704 – 711. · Zbl 0223.13006 · doi:10.4153/CJM-1971-079-5
[24] Stephen McAdam, Going down, Duke Math. J. 39 (1972), 633 – 636. · Zbl 0252.13001
[25] Stephen McAdam, Going down and open extensions, Canad. J. Math. 27 (1975), 111 – 114. · Zbl 0269.13004 · doi:10.4153/CJM-1975-013-5
[26] -, Simple going down, J. London Math. Soc. (to appear). · Zbl 0494.13002
[27] Masayoshi Nagata, Local rings, Interscience Tracts in Pure and Applied Mathematics, No. 13, Interscience Publishers a division of John Wiley & Sons New York-London, 1962. · Zbl 0123.03402
[28] I. J. Papick, Classes of going-down domains, Ph. D. Dissertation, Rutgers University, New Brunswick, N. J., 1974. · Zbl 0307.13001
[29] Michel Raynaud, Anneaux locaux henséliens, Lecture Notes in Mathematics, Vol. 169, Springer-Verlag, Berlin-New York, 1970 (French). · Zbl 0203.05102
[30] Fred Richman, Generalized quotient rings, Proc. Amer. Math. Soc. 16 (1965), 794 – 799. · Zbl 0145.27406
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.