Differential dimension polynomials of finitely generated extensions

Author:
William Sit

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

MSC:
Primary 12H05

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-London, 1973. Pure and Applied Mathematics, Vol. 54. MR**0568864****[2]**Joseph Johnson,*Differential dimension polynomials and a fundamental theorem on differential modules*, Amer. J. Math.**91**(1969), 239–248. MR**0238822****[3]**-,*Systems of n partial differential equations in n unknown functions*(manuscript).**[4]**Barbara 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**, 10.1090/S0002-9947-1970-0279079-1**[5]**T. S. Tomasovic,*A generalised Jacobi conjecture for arbitrary systems of algebraic differential equations*, Ph. D. dissertation, Columbia University, 1976.**[6]**William Yu Sit,*Typical differential dimension of the intersection of linear differential algebraic groups*, J. Algebra**32**(1974), no. 3, 476–487. MR**0379455****[7]**William Yu Sit,*Well-ordering of certain numerical polynomials*, Trans. Amer. Math. Soc.**212**(1975), 37–45. MR**0406992**, 10.1090/S0002-9947-1975-0406992-9

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DOI:
http://dx.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