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Bemerkungen über normale Flachheit und normale Torsionsfreiheit und Anwendungen. (German) Zbl 0431.13007


MSC:

13C11 Injective and flat modules and ideals in commutative rings
13C12 Torsion modules and ideals in commutative rings
13H99 Local rings and semilocal rings
13A15 Ideals and multiplicative ideal theory in commutative rings
14M12 Determinantal varieties
14M15 Grassmannians, Schubert varieties, flag manifolds
13H05 Regular local rings

Citations:

Zbl 0122.386
Full Text: DOI

References:

[1] M. F. Atiyah andI. G. Macdonald,Introduction to commutative algebra, Addison–Wesley, Reading, 1969.MR 39 # 4129 · Zbl 0175.03601
[2] R. C. Cowsik andM. V. Nori, On the fibres of blowing up,J. Indian Math. Soc. 40 (1976), 217–222.MR 58#28011 · Zbl 0437.14028
[3] J. A. Eagon, Examples of Cohen–Macaulay rings which are not Gorenstein,Math. Z. 109 (1969), 109–111.MR 39 # 5552 · Zbl 0184.29201 · doi:10.1007/BF01111241
[4] D. Eisenbud, M. Herrmann andW. Vogel, Remarks on regular sequences,Nagoya Math. J. 67 (1977), 177–180.MR 56 # 2999 · Zbl 0336.13014
[5] W. Gröbner,Matrizenrechnung (Hochschultaschenbücher 103/103a), Bibliographisches Institut, Mannheim, 1966.MR 33 # 7348
[6] W. Gröbner,Moderne algebraische Geometrie, Springer, Wien, 1949.MR 11–536 · Zbl 0033.12706
[7] W. Gröbner, Über Veronesesche Varietäten und deren Projektionen,Arch. Math. (Basel)16 (1965), 257–264.MR 32 # 1191 · Zbl 0135.21105
[8] W. Gröbner, Brief vom 14.9.1969 an B. Renschuch.
[9] A. Grothendieck,Éléments de géométrie algébrique, IV/1 (Inst. Hautes Études Sci. Publ. Math. No. 20), Paris, 1964.MR 30 # 3885
[10] A. Grothendieck,Éléments de géométrie algébrique, IV/2 (Inst. Hautes Études Sci. Publ. Math. No. 24), Paris, 1965.MR 33 # 7330
[11] A. Grothendieck,Éléments de géométrie algébrique, IV/1 (Inst. Hautes Études Sci. Publ. Math. No. 32), Paris, 1967.MR 39 # 220
[12] R. Hartsthorne, Complete intersections and connectedness,Amer. J. Math. 84 (1962), 497–508.MR 26 # 116 · Zbl 0108.16602 · doi:10.2307/2372986
[13] M. Herrmann, R. Schmidt undW. Vogel,Theorie der normalen Flachheit, Teubner, Leipzig, 1977.Zbl 356. 13008 · Zbl 0356.13008
[14] M. Herrmann undW. Vogel,Zur Theorie der normalen Flachheit, Universitäten Berlin und Halle, 1975. (Preprint)
[15] W. Hesselink, Depth and normal flatness, two examples,Math. Nachr. 79 (1977), 189–191.MR 57 # 12493 · Zbl 0364.13011 · doi:10.1002/mana.19770790115
[16] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero, I,Ann. of Math. 79 (1964), 109–203.MR 33 # 7333 · Zbl 0122.38603 · doi:10.2307/1970486
[17] M. Hochster, Criteria for equality of ordinary and symbolic powers of primes,Math. Z. 133 (1973), 53–65.MR 48 # 2127 · doi:10.1007/BF01226242
[18] M. Hochster, Grassmannians and their Schubert subvarieties are arithmetically Cohen–Macaulay,J. Algebra 25 (1973), 40–57.MR 47 # 3383 · Zbl 0256.14024 · doi:10.1016/0021-8693(73)90074-4
[19] M. Hochster andJ. A. Eagon, Cohen–Macaulay rings, invariant theory, and the generic perfection of determinantal loci,Amer. J. Math. 93 (1971), 1020–1058.MR 46 # 1787 · Zbl 0244.13012 · doi:10.2307/2373744
[20] H. Matsumura,Commutative algebra, Benjamin, New York, 1970.MR 42 # 1813 · Zbl 0211.06501
[21] T. Matsuoka, On an invariant of Veronesean rings,Proc. Japan Acad. 50 (1974), 287–291.MR 51 # 5588 · Zbl 0302.13015 · doi:10.3792/pja/1195518985
[22] B. Renschuch, Syzygienketten von Idealpotenzen,Zeszyty Nauk. Wy\.z. Szkol. Ped. Opol. 9 (1971), 85–96.Zbl 235. 13001
[23] B. Renschuch, Beiträge zur konstruktiven Theorie der Polynomideale, I,Wiss. Z. Pädagog. Hochsch. ”Karl Liebknecht” (Potsdam)17 (1973), 141–146.MR 49 # 10688a · Zbl 0279.13003
[24] B. Renschuch, Beiträge zur konstruktiven Theorie der Polynomideale, II,Wiss. Z. Pädagog. Hochsch. ”Karl Liebknecht” (Potsdam)17 (1973), 147–151.MR 49 # 10688b · Zbl 0279.13003
[25] B. Renschuch, Beiträge zur konstruktiven Theorie der Polynomideale, III,Wiss. Z. Pädagog. Hochsch. ”Karl Liebknecht” (Potsdam)17 (1973), 151–153.MR 49 # 10688c · Zbl 0279.13003
[26] B. Renschuch undE. Matuatat, Beiträge zur konstruktiven Theorie der Polynomideale, IV,Wiss. Z. Pädagog. Hochsch. ”Karl Liebknecht” (Potsdam)18 (1974), 95–98.MR 56 # 3009
[27] B. Renschuch, Beiträge zur konstruktiven Theorie der Polynomideale, V,Wiss. Z. Pädagog. Hochsch. ”Karl Liebknecht” (Potsdam)18 (1974), 98–100.MR 56 # 3010
[28] B. Renschuch, Beiträge zur konstruktiven Theorie der Polynomideale, VI,Wiss. Z. Pädagog. Hochsch. ”Karl Liebknecht” (Potsdam)18 (1974), 100–106.MR 56 # 3011
[29] L. Robbiano andG. Valla, Primary powers of a prime ideal,Pacific J. Math. 63 (1976), 491–498.MR 53 # 13247 · Zbl 0308.13003
[30] L. Robbiano andG. Valla, On normal flatness and normal torsion-freeness,J. Algebra 43 (1976), 552–560.MR 55 # 349 · Zbl 0349.13004 · doi:10.1016/0021-8693(76)90126-5
[31] B. Singh, A numerical criterion for the permissibility of a blowing-up,Compositio Math. 33 (1976), 15–28.MR 54 # 7456 · Zbl 0335.14003
[32] R. P. Stanley, Hilbert functions of graded algebras,Adv. in Math. 28 (1978), 57–83.Zbl 384. 13012 · Zbl 0384.13012 · doi:10.1016/0001-8708(78)90045-2
[33] J. Stückrad undW. Vogel, Über das Amsterdamer Programm von W. Gröbner und Buchsbaum Varietäten,Monatsh. Math. 78 (1974), 433–445.Zbl 297. 14002 · Zbl 0297.14002 · doi:10.1007/BF01295487
[34] T. Svanes, Coherent cohomology on Schubert subschemes of flag schemes and applications,Adv. in Math. 14 (1974), 369–453.MR 54 # 7490 · Zbl 0308.14008 · doi:10.1016/0001-8708(74)90039-5
[35] W. Vogel, Idealtheoretische Ordnungsbestimmung des Schnittes einer Veroneseschen Varietät,Arch. Math. (Basel)21 (1970), 567–570.MR 44 # 210 · Zbl 0221.13001
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