Jacobi's bound for the order of systems of first order differential equations

Author:
Barbara A. Lando

Journal:
Trans. Amer. Math. Soc. **152** (1970), 119-135

MSC:
Primary 12.80

DOI:
https://doi.org/10.1090/S0002-9947-1970-0279079-1

MathSciNet review:
0279079

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a system of differential polynomials in the differential indeterminates , and let be an irreducible component of the differential variety . If , there arises the question of securing an upper bound for the order of in terms of the orders of the polynomials in . It has been conjectured that the Jacobi number

**[1]**Claude Chevalley,*Introduction to the Theory of Algebraic Functions of One Variable*, Mathematical Surveys, No. VI, American Mathematical Society, New York, N. Y., 1951. MR**0042164****[2]**Richard M. Cohn,*Difference algebra*, Interscience Publishers John Wiley & Sons, New York-London-Sydeny, 1965. MR**0205987****[3]**Nathan Jacobson,*Lectures in abstract algebra. Vol III: Theory of fields and Galois theory*, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London-New York, 1964. MR**0172871****[4]**Serge Lang,*Introduction to algebraic geometry*, Interscience Publishers, Inc., New York-London, 1958. MR**0100591****[5]**J. F. Ritt,*Jacobi’s problem on the order of a system of differential equations*, Ann. of Math. (2)**36**(1935), no. 2, 303–312. MR**1503224**, https://doi.org/10.2307/1968572**[6]**-,*Differential algebra*, Amer. Math. Soc. Colloq. Publ., vol. 33, Amer. Math. Soc., Providence, R. I., 1950. MR**12**, 7.**[7]**Oscar Zariski and Pierre Samuel,*Commutative algebra, Volume I*, The University Series in Higher Mathematics, D. Van Nostrand Company, Inc., Princeton, New Jersey, 1958. With the cooperation of I. S. Cohen. MR**0090581****[8]**Oscar Zariski and Pierre Samuel,*Commutative algebra. Vol. II*, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N. J.-Toronto-London-New York, 1960. MR**0120249**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1970-0279079-1

Keywords:
Differential polynomial,
Jacobi bound,
differential kernel,
specialization,
dimension,
order of an irreducible differential variety

Article copyright:
© Copyright 1970
American Mathematical Society