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Some applications of differential algebra to ring theory


Authors: John Cozzens and Joseph Johnson
Journal: Proc. Amer. Math. Soc. 31 (1972), 354-356
DOI: https://doi.org/10.1090/S0002-9939-1972-0289472-6
MathSciNet review: 0289472
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Abstract | References | Additional Information

Abstract: It is shown that simple noetherian $ V$-domains with a unique simple module can have any global homological dimension.


References [Enhancements On Off] (What's this?)

  • [1] John H. Cozzens, Homological properties of the ring of differential polynomials Bull. Amer. Math. Soc. 76 (1970), 75-79. MR 41 #3531. MR 0258886 (41:3531)
  • [2] Joseph Johnson, Extensions of differential modules over formal power series rings, Amer. J. Math. 93 (1971), 731-741. MR 0294310 (45:3379)
  • [3] -, Differential dimension polynomials and a fundamental theorem on differential modules, Amer. J. Math. 91 (1969), 239-248. MR 39 #186. MR 0238822 (39:186)
  • [4] Ellis R. Kolchin, Galois theory of differential fields, Amer. J. Math. 75 (1953), 753-824. MR 15, 394; 1140. MR 0058591 (15:394a)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0289472-6
Keywords: Differential algebra, rings of linear differential operators, $ V$-ring, universal differential field, global homological dimension
Article copyright: © Copyright 1972 American Mathematical Society

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