Going Down in Polynomial Rings

Abstract

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.