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On a change of rings for mixed multiplicities

Truong Thi Hong Thanh|Duong Quoc Viet
대한수학회 (The Korean Mathematical Society)|2020.09|대한수학회보 (Bulletin of the KMS)|제57권 제5호|pp. 1251-1258|DOI 10.4134/BKMS.b190914

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참고문헌

키워드

Noetherian ringMixed multiplicityHilbert-Samuel multiplicity
주제분류수학

초록

This paper establishes a formula changing the ring from a Noetherian local ring $A$ of dimension $d > 0$ containing the residue field $k$ to the polynomial ring in $d$ variables $k[X_1, X_2,\ldots, X_d]$ for mixed multiplicities. And as consequences, we get a formula for the multiplicity of Rees rings and formulas for mixed multiplicities and the multiplicity of Rees rings of quotient rings of $A$ by highest dimensional associated prime ideals of $A$.

Abstract

This paper establishes a formula changing the ring from a Noetherian local ring $A$ of dimension $d > 0$ containing the residue field $k$ to the polynomial ring in $d$ variables $k[X_1, X_2,\ldots, X_d]$ for mixed multiplicities. And as consequences, we get a formula for the multiplicity of Rees rings and formulas for mixed multiplicities and the multiplicity of Rees rings of quotient rings of $A$ by highest dimensional associated prime ideals of $A$.

참고문헌 (32)

  1. M. F. Atiyah, "Introduction to Commutative Algebra" (1969), Addison-Wesley Publishing Co
  2. W. Bruns, "Cohen-Macaulay Rings" (1993), Cambridge University Press
  3. E. Boda, "A note on the computation of multiplicities", Beitrage Algebra Geom, 45(1), pp.183~190 (2004)
  4. R. Callejas-Bedregal, "Mixed multiplicities and the minimal number of generator of modules", Journal of Pure and Applied Algebra, 214(9), pp.1642~1653 (2010), Elsevier BV[DOI]
  5. L. V. Dinh, "On some superficial sequences", Southeast Asian Bull. Math, 38(6), pp.803~811 (2014)
  6. L. V. Dinh, "On two results of mixed multiplicities", Int. J. Algebra, 4(1-4), pp.19~23 (2010)
  7. Manfred Herrmann, "Reduction Numbers and Multiplicities of Multigraded Structures", Journal of Algebra, 197(2), pp.311~341 (1997), Elsevier BV[DOI]
  8. C. Huneke, "Integral Closure of Ideals, Rings, and Modules" (2006), Cambridge University Press
  9. Daniel Katz, "Extended Rees algebras and mixed multiplicities", Mathematische Zeitschrift, 202(1), pp.111~128 (1989), Springer Science and Business Media LLC[DOI]
  10. S. Kleiman, "Mixed Buchsbaum-Rim multiplicities", Amer. J. Math, 118(3), pp.529~569 (1996)
  11. N. T. Ma. nh, "Mixed multiplicities of modules over Noetherian local rings", Tokyo J. Math, 29(2), pp.325~345 (2006)[DOI]
  12. D. Rees, "Generalizations of reductions and mixed multiplicities", J. London Math. Soc, 29(3), pp.397~414 (1984)[DOI]
  13. I. Swanson, "Mixed multiplicities, joint reductions and quasi-unmixed local rings", J. London Math. Soc, 48(1), pp.1~14 (1993)[DOI]
  14. B. Teissier, "Singularites a Cargese", pp.285~362 (1973), Soc. Math
  15. Truong Thi Hong Thanh, "Mixed multiplicities of maximal degrees", 대한수학회지, 55(3), pp.605~622 (2018), 대한수학회
  16. Truong Thi Hong Thanh, "Mixed multiplicities and the multiplicity of Rees modules of reductions", Journal of Algebra and Its Applications, 18(09), pp.1950176~ (2019), World Scientific Pub Co Pte Lt[DOI]
  17. J.K. Verma, "Multigraded Rees algebras and mixed multiplicities", Journal of Pure and Applied Algebra, 77(2), pp.219~228 (1992), Elsevier BV[DOI]
  18. Duong Quôc Viêt, "Mixed multiplicities of arbitrary ideals in local rings", Communications in Algebra, 28(8), pp.3803~3821 (2000), Informa UK Limited[DOI]
  19. Duong Quôc Viêt, "Sequences Determining Mixed Multiplicities and Reductions of Ideals", Communications in Algebra, 31(10), pp.5047~5069 (2003), Informa UK Limited[DOI]
  20. Duong Quôc Viêt, "Reductions and Mixed Multiplicities of Ideals", Communications in Algebra, 32(11), pp.4159~4178 (2006), Informa UK Limited[DOI]
  21. Duong Quôc Viê.t, "The multiplicity and the Cohen–Macaulayness of extended Rees algebras of equimultiple ideals", Journal of Pure and Applied Algebra, 205(3), pp.498~509 (2006), Elsevier BV[DOI]
  22. Duong Quôc Việt, "On the Cohen-Macaulayness of fiber cones", Proceedings of the American Mathematical Society, 136(12), pp.4185~4195 (2008), American Mathematical Society (AMS)[DOI]
  23. Duong Quoc VIET, "ON THE MULTIPLICITY OF REES ALGEBRAS OF GOOD FILTRATIONS", Kyushu Journal of Mathematics, 66(2), pp.261~272 (2012), Faculty of Mathematics, Kyushu University[DOI]
  24. Duong Quoc Viet, "On Mixed Multiplicities of Good Filtrations", Algebra Colloquium, 22(03), pp.421~436 (2015), World Scientific Pub Co Pte Lt[DOI]
  25. Duong Quoc Viet, "A note on joint reductions and mixed multiplicities", Proceedings of the American Mathematical Society, 142(6), pp.1861~1873 (2014), American Mathematical Society (AMS)[DOI]
  26. D. Q. Viet, "On the multiplicity of multigraded modules over Artinian local rings", Tokyo J. Math, 33(2), pp.341~360 (2010)[DOI]
  27. Duong Quoc Viet, "Mixed multiplicities of multigraded modules", Forum Mathematicum, 25(2), pp.337~361 (2013), Walter de Gruyter GmbH[DOI]
  28. Duong Quoc VIET, "MULTIPLICITY AND COHEN-MACAULAYNESS OF FIBER CONES OF GOOD FILTRATIONS", Kyushu Journal of Mathematics, 65(1), pp.1~13 (2011), Faculty of Mathematics, Kyushu University[DOI]
  29. D. Q. Viet, "On(FC)-sequences and mixed multiplicities of multi-graded algebras", Tokyo J. Math, 34(1), pp.185~202 (2011)[DOI]
  30. Duong Quoc Viet, "On some multiplicity and mixed multiplicity formulas", Forum Mathematicum, 26(2), pp.413~442 (2014), Walter de Gruyter GmbH[DOI]
  31. Duong Quoc Viet, "A note on formulas transmuting mixed multiplicities", Forum Mathematicum, 26(6), pp.1837~1851 (2014), Walter de Gruyter GmbH[DOI]
  32. Duong Quoc VIET, "THE EULER-POINCARÉ CHARACTERISTIC AND MIXED MULTIPLICITIES", Kyushu Journal of Mathematics, 69(2), pp.393~411 (2015), Faculty of Mathematics, Kyushu University[DOI]

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