General Theory of Primes
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  • 作者:Hidetoshi Marubayashi (1)
    Fred Van Oystaeyen (2)
  • 刊名:Lecture Notes in Mathematics
  • 出版年:2012
  • 出版时间:2012
  • 年:2012
  • 卷:2059
  • 期:1
  • 页码:109-173
  • 全文大小:963KB
  • 参考文献:1. G.Q. Abbasi, S. Kobayashi, H. Marubayashi, A. Ueda, Noncommutative unique factorization rings. Comm. Algebra 19(1), 167-98 (1991)
    2. F. Aly, F. Van Oystaeyen, Hopf filtrations and Larson-type orders in Hopf algebras. J. Algebra 267, 756-72 (2004)
    3. C. Baetica, F. Van Oystaeyen, Valuation extensions of filtered and graded algebras. Comm. Algebra 34, 829-40 (2006)
    4. K. Brown, H. Marubayashi, P.F. Smith, Group rings which are v-HC orders and Krull orders. Proc. Edinb. Math. Soc. 34, 217-28 (1991)
    5. H. Brungs, N. Dubrovin, A Classification and examples of rank one chain domains. Trans. Am. Math. Soc. 335(7), 2733-753 (2003)
    6. H. Brungs, H. Marubayashi, E. Osmanagic, A classification of prime segments in simple Artinian rings. Proc. Am. Math. Soc. 128(11), 3167-175 (2000)
    7. H. Brungs, H. Marubayashi, E. Osmanagic, Gauss extensions and total graded subrings for crossed product algebras. J. Algebra 316, 189-05 (2007)
    8. H. Brungs, H. Marubayashi, E. Osmanagic, Primes of Gauss extensions over crossed product algebras. Comm. Algebra 40(6), (2012)
    9. H. Brungs, H. Marubayashi, A. Ueda, A Classification of primary ideals of Dubrovin valuation rings. Houston J. Math. 29(3), 595-08 (2003)
    10. H. Brungs, G. T?rmer, Extensions of chain rings. Math. Z. 185, 93-04 (1984)
    11. S. Caenepeel, M. Van den Bergh, F. Van Oystaeyen, Generalized crossed products applied to maximal orders, Brauer groups and related exact sequences. J. Pure Appl. Algebra 33(2), 123-49 (1984)
    12. G. Cauchon, Les T-anneaux et les anneaux à identités polynomials Noethé riens, Thèse de doctorat, Université Paris XI, 1977
    13. M. Chamarie, Anneaux de Krull non commutatifs, Thèse, Univ. de Lyon, 1981
    14. M. Chamarie, Anneaux de Krull non commutatifs. J. Algebra 72, 210-22 (1981)
    15. M. Chamarie, / Sur les orders maximaux au sense d’Asano, Vorlesungen aus dem Fachbereich Mathematik der Univ. Essen, Heft 3 (1979)
    16. A. Chatters, C. Hajarnavis, / Rings with Chain Conditions. Research Notes in Mathematics, vol. 44 (Pitman, London, 1980)
    17. C. Chevalley, / Introduction to the Theory of Algebraic Functions of One Variable. Mathematical Surveys, vol. VI (American Mathematical Society, New York, 1951)
    18. P.M. Cohn, / Skew Field Constructions. London Mathematical Society, vol. 27 (Cambridge University Press, London, 1977)
    19. I. Connell, Natural transform of the spec functor. J. Algebra 10, 69-1 (1968)
    20. S. Dascalescu, C. Nǎstǎsescu, S. Raianu, / Hopf Algebras. Pure and Applied Mathematics, vol. 235 (M. Dekker, New York, 2001)
    21. N. Dubrovin, Noncommutative valuation rings. Trans. Moscow Math. Soc. 45, 273-87 (1984)
    22. O. Endler, / Valuation Theory(Springer, Berlin, 1972)
    23. L. Fuchs, / Teilweise Geordnete Algebraische Strukturen, Vandenhoeck and Ruprecht, G?ttingen, 1966
    24. P. Gabriel, R. Rentschler, Sur la dimension des anneaux et ensembles ordonnées. C. R. Acad. Paris 265, 712-15 (1967)
    25. R. Gilmer, / Multiplicative Ideal Theory. Queens-Papers in Pure and Applied Mathematics, vol. 90 (Queens-University, Kingston, 1992)
    26. A. Goldie, / The Structure of Noetherian Rings. Lecture Notes in Mathematics, vol. 246 (Springer, Berlin, 1972)
    27. R. Gordon, J.C. Robson, / Krull Dimension. Memoirs American Mathematical Society, vol.?133 (1973)
    28. D. Haile, P. Morandi, On Dubrovin valuation rings in crossed product algebras. Trans. Am. Math. Soc. 338, 723-51 (1993)
    29. C. Hajarnavis, T. Lenagan, Localization in Asano orders. J. Algebra 21, 441-49 (1972)
    30. D. Harrisson, / Finite and Infinite Primes for Rings and Fields. Memoirs of the American Mathematical Society, vol. 68 (1968)
    31. C. Kassel, / Quantum Groups. Graduate Texts in Mathematics, vol. 155 (Springer, Berlin, 1995)
    32. J. Kauta, H. Marubayashi, H. Miyamoto, Crossed product orders over valuation rings II. Bull. Lond. Math. Soc. 35, 541-52 (2003)
    33. S. Kobayashi, H. Marubayashi, N. Popescu, C. Vracin, G. Xie, Noncommutative valuation rings of the quotient Artinian ring of a skew polynomial ring. Algebra Rep. Theor. 8, 57-8 (2005)
    34. G. Krause, T. Lenagan, / Growth of Algebras and Gelfand-Kirillov Dimension. Research Notes in Mathematics, vol. 116 (Pitman, London, 1985)
    35. R. Larsson, Hopf algebra orders determined by group valuations. J. Algebra 38, 414-52 (1976)
    36. L. Le Bruyn, F. Van Oystaeyen, A note on noncommutative Krull domains. Comm. Algebra 14(8), 1457-472 (1986)
    37. L. Le Bruyn, F. Van Oystaeyen, Generalized Rees rings and relative maximal orders satisfying polynomial identities. J. Algebra 83(2), 409-36 (1993)
    38. L. Le Bruyn, M. Van den Bergh, F. Van Oystaeyen, / Graded Orders(Birkhauser, Boston, 1988)
    39. H. Li, F. Van Oystaeyen, Filtrations on simple Artinian rings. J. Algebra 232, 361-71 (1990)
    40. H. Li, F. Van Oystaeyen, / Zariskian Filtration. K-Monographs in Mathematics, vol. 2 (Kluwer Academic, Dordrecht, 1996)
    41. H. Marubayashi, H. Miyamoto, A. Ueda, / Noncommutative Valuation Rings and Semi-hereditary Orders. K-Monographs in Mathematics, vol. 3 (Kluwer Academic, Dordrecht, 1997)
    42. H. Marubayashi, E. Nauwelaerts, F. Van Oystaeyen, Graded rings over arithmatical orders. Comm. Algebra 12, 745-75 (1984)
    43. H. Marubayashi, G. Xie, A classification of graded extensions in a skew Laurent polynomial ring. J. Math. Soc. Jpn. 60(2), 423-43 (2008)
    44. H. Marubayashi, G. Xie, A classification of graded extensions in a skew Laurent polynomial ring, II. J. Math. Soc. Jpn. 61(4), 1111-130 (2009)
    45. K. Mathiak, Bewertungen nicht kommutativer K?rper. J. Algebra 48, 217-35 (1977)
    46. G. Maury, J. Raynand, / Ordres maximaux au sense de K. Asano. Lecture Notes in Mathematics, vol. 808 (Springer, Berlin, 1980)
    47. J. McConnell, J.C. Robson, / Noncommutative Noetherian Rings(Wiley-Interscience, New York, 1987)
    48. G. Michler, Asano orders. Proc. Lond. Math. Soc. 3, 421-43 (1969)
    49. H. Moawad, F. Van Oystaeyen, Discrete valuations extend to certain algebras of quantum type. Comm. Algebra 24(8), 2551-566 (1996)
    50. C. Nǎstǎsescu, E. Nauwelaerts, F. Van Oystaeyen, Arithmetically graded rings revisited. Comm. Algebra 14(10), 1991-007 (1986)
    51. C. Nǎstǎsescu, F. Van Oystaeyen, / Graded and Filtered Rings and Modules. Lecture Notes in Mathematics, vol. 758 (Springer, Berlin 1979)
    52. C. Nǎstǎsescu, F. Van Oystaeyen, / Graded Ring Theory(North Holland, Dordrecht, 1982)
    53. C. Nǎstǎsescu, F. Van Oystaeyen, / Dimensions of Ring Theory. Mathematics and Its Applications, vol. 36 (D. Reidel Publ. Co., Dordrecht, 1987)
    54. E. Nauwelaerts, F. Van Oystaeyen, / Localization at Primes in Algebras over Fields. Indag. Math. 39, 233-42 (1977)
    55. E. Nauwelaerts, F. Van Oystaeyen, Finite generalized crossed products over Tame and maximal orders. J. Algebra 101(1), 61-8 (1986)
    56. D. Passman, / Infinite Crossed Products. Pure and Applied Mathematics, vol. 135 (Academic, New York, 1987)
    57. I. Reiner, / Maximal Orders. London Mathematical Society, Monographs Series, vol. 5 (Academic, New York, 1975)
    58. J.C. Robson, Noncommutative Dedekind rings. J. Algebra 9, 249-65 (1968)
    59. J. Rotman, / Notes on Homological Algebra(Van Nostrand Reinhold, New York, 1970)
    60. H. Rutherford, Characterizing primes in some noncommutative rings. Pac. J. Math. 27, 387-92 (1968)
    61. O. Schilling, / The Theory of Valuations. Mathematical Surveys and Monographs, vol. 4 (American Mathematical Society, Providence, 1950)
    62. Ya.I. Shtipel’man, Valuations on the quotient field of the ring of quantum mechanics. Funkts. Anal. Pnlozh. 71(1), 56-3 (1973)
    63. B. Stenstr?m, / Rings of Quotients(Springer, Berlin, 1975)
    64. B. Torrecillas, F. Van Oystaeyen, Divisorially graded rings, related groups and sequences. J.?Algebra 105(2), 411-28 (1978)
    65. M. Van den Bergh, F. Van Oystaeyen, Lifting maximal orders. Comm. Algebra 17(2), 341-49 (1989)
    66. J.P. Van Deuren, F. Van Oystaeyen, / Arithmetically Graded Rings I. Lecture Notes in Mathematics, vol. 825 (Springer, Berlin, 1980), pp.?130-52
    67. J.P. Van Deuren, J. Van Geel, F. Van Oystaeyen, / Genus and a Riemann-Roch Theorem for Noncommutative Function Fields in Ore Variable. Lecture Notes in Mathematics, vol. 867 (Springer, Berlin, 1981), pp.?295-18
    68. J. Van Geel, / A Noncommutative Theory for Primes. Lecture Notes in Pure and Applied Mathematics, vol. 51 (M. Dekker, New York, 1979), pp.?767-81
    69. J. Van Geel, / Places and Valuations in Noncommutative Ring Theory. Lecture Notes in Pure and Applied Mathematics, vol. 71 (M. Dekker, New York, 1981)
    70. F. Van Oystaeyen, On pseudo-places of algebras. Vull. Soc. Math. Belg. 25, 139-59 (1973)
    71. F. Van Oystaeyen, Primes in algebras over fields. Pure Appl. Algebra 5, 239-52 (1974)
    72. F. Van Oystaeyen, / Prime Spectra in Noncommutative Algebra. Lecture Notes in Mathematics, vol. 444 (Springer, Berlin, 1975)
    73. F. Van Oystaeyen, Crossed products over arithmetically graded rings. J. Algebra 80(2), 537-51 (1983)
    74. F. Van Oystaeyen, On orders over graded Krull domains. Osaka J. Math. 20(4), 757-65 (1983)
    75. F. Van Oystaeyen, / Algebraic Geometry for Associative Algebras. Monographs in Pure and Applied Mathematics, vol. 227 (M. Dekker, New York, 2000)
    76. F. Van Oystaeyen, A. Verschoren, / Noncommutative Algebraic Geometry, an Introduction. Lecture Notes in Mathematics, vol. 887 (Springer, Berlin, 1981)
    77. F. Van Oystaeyen, A. Verschoren, / Relative Invariants of Rings; The Noncommutative Theory. Monographs in Pure and Applied Mathematics, vol. 86 (M. Dekker, New York, 1984)
    78. F. Van Oystaeyen, L. Willaert, Valuations on extensions of Weyl skew fields. J. Algebra 183, 359-64 (1996)
    79. H. Warner, Finite primes in simple algebras. Pac. J. Math. 36, 245-65 (1971)
    80. L. Willaert, Discrete valuations on Weyl skew fields. J. Algebra 187(2), 537-47 (1997)
    81. E. Witt, Riemann-Rochser Satz und z-Funktionen in Hyperkomplexen. Math. Ann. 110, 12-8 (1934)
    82. O. Zariski, P. Samuel, / Commutative Algebra I. Graduate Texts in Mathematics, vol. 28 (Springer, Berlin, 1958)
  • 作者单位:Hidetoshi Marubayashi (1)
    Fred Van Oystaeyen (2)

    1. Faculty of Science and Engineering Shido, Tokushima Bunri University, Sanuki City, Kagawa, Japan
    2. Mathematics and Computer Science, University of Antwerp, Antwerp, Belgium
文摘
Throughout we fix notation and conventions as follows. By Rwe denote an associative ring with unit and R-/em>is a subring of R.

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