Studies in Rings generalised Unique Factorisation Rings

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In chapter 4,
theorem 4.35 assures the right
second layer condition for height one prime ideals
in a GUFR. The right second layer condition for a
prime ideal of height> 1 in a GUFR
is yet to be
discussed. Also, it is not yet investigated whether
{p €. Xr/Qr--t p} in theorem 4.4J, is always right
stable or not. However, from [26], it follows that,
in a GUFR
if every height 1 prime ideal is maximal,
then each XI
is right stable, satisfies the right
second layer condition (theorem 4.35) and the incomparability
condition.
It may be
possible to extend the concept of
GUFRs to (non-Noetherian) rings with (left and right)
Krull dimension [30]. The analogous nature of such
rings with Noetherian rings is a
major source of
interest in them. The invertible ideals, in rings
with (left and
right) Krull dimension, also behave
well o
A study of invertible ideals in rings with
Krull dimension is given in [31].