Prime Ideals in Noetherian Rings

Details Prime Ideals in Noetherian Rings Prime Ideals in Noetherian Rings

2011-11-26

arxiv.org/abs/1111.6141v1

Mathematics

Rings and Algebras

6 pages

Scientific paper

In this short note we study the links of certain prime ideals of a noetherian ring R. We first give the definition of a link krull symmetric noetherian ring R. We then prove theorem 9 that states that for any linked prime ideals P' and Q' of the polynomial ring R[X] where R is a link krull symmetric noetherian ring, if The prime ideal P' is extended then Q' is also an extended prime ideal of R[X]. An application of theorem 9 is then given in theorem 12 for the ring R[X] when R is assumed to be a fully bounded noetherian ring.

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