Studies in Rings generalised Unique Factorisation Rings

-4-
non zero prime ideal of R contains a non zero principal prime
ideal.
Since every domain is a
prime ring, this class of
rings contains the class of NUFDs.
The rings of this
class have aI.rnos t all properties of UFDs but the factorisation
can be done only for t.ho s e elements p wi t11 pR = Rp ,
Before entering into more details of the material
of this thesis we give a brief review of the preliminary
materials.
PRELllv\INARIES
Conventions
All the rings in this thesis are assumed to be
associative arid
they have identity elements unless it is
otherwise mentioned. To empha"size the order theoretic
na t ur e , we use "the notations of inequalities ~ , < , {
for 'contained in', 'properly contained in' and
'not
contained in' respectively.
We
begin with the basic equivalent conditions which
are abbreviated by "No e t.he r i an" honoring, Eo Noether, who