Differential dimension polynomials of finitely generated extensions

Author:
William Sit

Journal:
Proc. Amer. Math. Soc. **68** (1978), 251-257

MSC:
Primary 12H05

DOI:
https://doi.org/10.1090/S0002-9939-1978-0480353-7

MathSciNet review:
480353

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Abstract: Let be a finitely generated extension of a differential field with *m* derivative operators. Let *d* be the differential dimension of over . We show that the numerical polynomial

**[1]**E. R. Kolchin,*Differential algebra and algebraic groups*, Academic Press, New York, 1973. MR**0568864 (58:27929)****[2]**Joseph Johnson,*Differential dimension polynomials and a fundamental theorem on differential modules*, Amer. J. Math.**91**(1969), 239-248. MR**0238822 (39:186)****[3]**-,*Systems of n partial differential equations in n unknown functions*(manuscript).**[4]**B. A. Lando,*Jacobi's bound for the order of systems of first order differential equations*, Trans. Amer. Math. Soc.**152**(1970), 119-135. MR**0279079 (43:4805)****[5]**T. S. Tomasovic,*A generalised Jacobi conjecture for arbitrary systems of algebraic differential equations*, Ph. D. dissertation, Columbia University, 1976.**[6]**W. Y. Sit,*Typical differential dimension of the intersection of linear differential algebraic groups*, J. Algebra**32**(1974), 476-487. MR**0379455 (52:360)****[7]**-,*Well-ordering of certain numerical polynomials*, Trans. Amer. Math. Soc.**212**(1975), 37-45. MR**0406992 (53:10776)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1978-0480353-7

Keywords:
Differential dimension polynomials,
characteristic sets,
differential prime ideals,
differential polynomials,
ranking,
initial subsets

Article copyright:
© Copyright 1978
American Mathematical Society