Studies in Rings generalised Unique Factorisation Rings

-111-
Proof:
Put X = \ P E. Xr/Q ~ PJ 0
Since the elements
of X are height 1 prime ideals, X satisfies the right
second layer condition and the incomparability condition.
The sparsity of XI implies that X is finite
[16, theorem 6.2~14J and so X satisfies the right
intersection property. Now the rGsult follows from
theorem 4.23 and the hypothesis that X is right -st abLe ,
Frorn Th eo r ern 4.35 and __ . _. __~ 4. 25" it follows that
Theorem 4·.41.
Every finite right stable set consists of height 1
prime ideals in a GUFR
is right classically localisable.