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A Difference-Differential Basis Theorem

Published online by Cambridge University Press:  20 November 2018

Richard M. Cohn
Richard M. Cohn*
Affiliation:
Rutgers University, New Brunswick, New Jersey
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Our aim in this paper is to extend to difference-differential rings the beautiful theorem of Kolchin [5, Theorem 3] for the differential case. The necessity portion of Kolchin's result is not obtained.

What might well be called the Ritt basis theorem states that if a commutative ring R with identity is finitely generated over a subring R 0, then the ascending chain condition for radical ideals of R 0 implies the ascending chain condition for radical ideals of R. (This is indeed a basis theorem. If we define a basis for a radical ideal A to be a finite set B such that then every radical ideal of a ring R has a basis if and only if the ascending chain condition for radical ideals holds in R.) It is the Ritt basis theorem rather than the Hilbert basis theorem which has appropriate generalizations in differential and difference algebra, where in fact it originated.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 6 , 01 December 1970, pp. 1224 - 1237
Copyright
Copyright © Canadian Mathematical Society 1970

References

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