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Original Articles

Critical Modules of the Ring of Differential Operators of an Affine Semigroup Algebra

Pages 618-631 | Received 28 Apr 2008, Published online: 18 Feb 2010

REFERENCES

  • Eisenbud , D. ( 1995 ). Commutative Algebra with a View Toward Algebraic Geometry . Grad. Texts in Math. , Vol. 150 . New York : Springer-Verlag .
  • Gabriel , P. ( 1962 ). Des catégories abéliennes . Bull. Soc. Math. France 90 : 323 – 448 .
  • Goodearl , K. R. , Warfield , R. B. (1989). An Introduction to Noncommutative Noetherian Rings . London Math. Soc. Student Texts, Vol. 16 . Cambridge : Cambridge University Press.
  • Goldie , A. W. ( 1972 ). Properties of the idealiser . In: Gordon , R. , ed. Ring Theory . New York : Academic Press , pp. 161 – 169 .
  • Hart , R. ( 1971 ). Krull dimension and global dimension of simple Ore-extensions . Math. Zeitschrift 121 : 341 – 345 .
  • Lenagan , T. H. ( 2000 ). Dimension theory of Noetherian rings . In: Krause , H. , Ringel , C. , ed. Infinite Length Modules . (Bielefeld, 1998), Trends in Math. , Basel : Birkhäuser , pp. 129 – 148 .
  • McConnel , J. C. , Robson , J. C. ( 1987 ). Noncommutative Noetherian Rings . Chichester : John Wiley & Sons .
  • Musson , I. M. ( 1987 ). Rings of differential operators on invariant rings of tori . Trans. AMS 303 : 805 – 827 .
  • Musson , I. M. , Van den Bergh , M. ( 1998 ). Invariants Under Tori of Rings of Differential Operators and Related Topics . Mem. of the AMS 650 . Providence : Amer. Math. Soc.
  • Rentschler , R. , Gabriel , P. ( 1967 ). Sur la dimension des anneaux et ensembles ordonnés . C. R. Acad. Sci. Paris, Sér. A 265 : 712 – 715 .
  • Saito , M. ( 2001 ). Isomorphism classes of A-hypergeometric systems . Compos. Math. 128 : 323 – 338 .
  • Saito , M. ( 2007 ). Primitive ideals of the ring of differential operators on an affine toric variety . Tohoku Math. J. 59 : 119 – 144 .
  • Saito , M. , Takahashi , K. ( 2009 ). Noetherian properties of rings of differential operators of affine semigroup algebras . Osaka J. Math. 46 : 529 – 556 .
  • Saito , M. , Traves , W. N. ( 2001 ). Differential algebras on semigroup algebras . AMS Contem. Math. 286 : 207 – 226 .
  • Communicated by T. Lenagan.

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