Studies in Rings generalised Unique Factorisation Rings

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Jk < Qo Consequently J ~ Q, since Q is prime. Thus
I ~ Q, which contradicts the selection of Q. Therefore
P satisfies the right second layer condition.
Corollary 4.36.
Let P be a height 1 prime ideal of a GUFR such
that {p} is right stable. Then P is classically right
localisableo
Proof:
This is an immediate c ons equen c e of theorem 4.14
and theorem 4035.
A semiprime ideal S of a Noetherian ring is said
to be classically right localisable if the finite set
of prime ideals associated with S
is classically right
localisable. Thus we get another consequence of theorenl
4.35 and theorem 4.23.
Corollary 4.37.
Let S be a semiprime ideal in a GUFR and assume
that the associated prime ideals of S are height 1
prime ideals.
Suppose also that the collection of
associated primes is right stable.
Then S is classically
r i.qh t Lo c a.l i s a bl e ,