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PRIME AND POISSON PRIME IDEALS IN SKEW EXTENSIONS DETERMINED BY DERIVATIONS

  • Myung, No-Ho (Department of Mathematics Chungnam National University) ;
  • Oh, Sei-Qwon (Department of Mathematics Chungnam University)
  • Received : 2013.06.23
  • Accepted : 2013.09.27
  • Published : 2013.11.15

Abstract

Let R be a commutative noetherian algebra and let ${\delta}$ be a nonzero derivation. Here we determine the prime ideals of the skew polynomial algebra R[z;${\delta}$] and the Poisson prime ideals of R[z;${\delta}$]p.

Keywords

References

  1. J. Dixmier, Enveloping algebras, The 1996 printing of the 1977 English trans-lation Graduate Studies in Mathematics, vol. 11, American Mathematical Society, Providence, 1996.
  2. K. R. Goodearl, Prime ideals in skew polynomial rings and quantized Weyl algebras, J. Algebra 150 (1992), 324-377. https://doi.org/10.1016/S0021-8693(05)80036-5
  3. K. R. Goodearl, A Dixmier-Moeglin equivalence for Poisson algebras with torus actions, in Algebra and Its Applications (D. V. Huynh, S. K. Jain, and S. R. Lopez-Permouth, Eds.) Contemp. Math. 419 (2006), 131-154. https://doi.org/10.1090/conm/419/08001
  4. K. R. Goodearl and R. B. Warfield, An introduction to noncommutative noe-therian rings, London Mathematical Society Student Text 16, Cambridge University Press, 1989.
  5. S.-Q. Oh, Poisson polynomial rings, Comm. Algebra 34 (2006), 1265-1277. https://doi.org/10.1080/00927870500454463
  6. S.-Q. Oh, Poisson prime ideals of Poisson polynomial rings, Comm. Algebra 35 (2007), 3007-3012. https://doi.org/10.1080/00927870701404721