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Systems of Ideals

Published online by Cambridge University Press:  20 November 2018

Richard M. Cohn
Richard M. Cohn*
Affiliation:
Rutgers, The State University, New Brunswick, New Jersey
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Some well-known theorems on the representation of an ideal in a commutative ring as an intersection of ideals of a specified type remain valid when attention is restricted to certain subclasses of the ideals of the ring. For example, a homogeneous ideal in a graded Noetherian ring is the intersection of homogeneous primary ideals, and Seidenberg (16) has recently proved a similar result for differential rings. Other examples are provided by theorems on the representation of certain differential and difference ideals as intersections of prime differential or difference ideals.

Kolchin (6) began the development of a general theory applicable to such phenomena. In this paper, I continue the development of that theory.

In §§ 1 and 2, I have followed Kolchin's definition and discussion of divisible systems with minor modifications and additions.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 783 - 807
Copyright
Copyright © Canadian Mathematical Society 1969

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