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Going Down in Polynomial Rings

Published online by Cambridge University Press:  20 November 2018

Stephen McAdam
Stephen McAdam*
Affiliation:
The University of Texas, Austin, Texas
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In this paper, R ⊂ T will be commutative domains having a common identity.

Definition. Suppose that R is a subdomain of T.

(i) If P is a prime ideal of R and Q is a prime ideal of T, we say that Q lies over P if Q ∩ R = P.

(ii) If every prime of R has a prime of T lying over it, we say that R ⊂ T has lying over.

(iii) If there is a unique prime of T lying over P in R, we say that P is unibranched in T.

(iv) If every prime of R is unibranched in T we say that R ⊂ T is unibranched.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 23 , Issue 4 , August 1971 , pp. 704 - 711
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Kaplansky, I., Commutative rings (Allyn and Bacon, Boston, 1970).Google Scholar
2. McAdam, S., Going down (to appear).Google Scholar