Differential algebra is a field of mathematics that attempts to use methods from abstract algebra to study solutions of systems of polynomial nonlinear ordinary and partial differential equations. It is a generalization of classical commutative algebra and is primarily based on the work of Ritt (1950) and Kolchin (1973). Mansfield (1991) gave a terminating algorithm for differential Gröbner bases, which are differential analogs of polynomial Gröbner bases.

# Differential Algebra

## See also

Abstract Algebra, Commutative Algebra, Differential, Differential-Algebraic Equation, Gröbner Basis
*This entry contributed by Bhuvanesh
Bhatt*

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## References

Kolchin, E. R.*Differential Algebra and Algebraic Groups.*New York: Academic Press, 1973.Mansfield, E. L.

*Differential Gröbner Bases.*Ph.D. thesis, University of Sydney, 1991.Ritt, J. F.

*Differential Algebra.*Providence, RI: Amer. Math. Soc., 1950. http://www.ams.org/online_bks/coll33/.

## Referenced on Wolfram|Alpha

Differential Algebra## Cite this as:

Bhatt, Bhuvanesh. "Differential Algebra." From *MathWorld*--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/DifferentialAlgebra.html