Student Number : 9206749J -
PhD thesis -
School of Mathematics -
Faculty of Science / For right near-rings the left representation has always been considered the
natural one. A study of right representation for right distributively generated
(d.g.) near-rings was initiated by Rahbari and this work is extended
here to introduce radical-like objects in the near-ring R using right R-groups.
The right radicals rJ0(R), rJ1/2(R) and rJ2(R) are defined as counterparts
of the left radicals J0(R), J1/2(R) and J2(R) respectively, and their properties
are discussed. Of particular interest are the relationships between the left
and right radicals. It is shown for example that for all finite d.g. near-rings
R with identity, J2(R) = rJ0(R) = rJ1/2(R) = rJ2(R). A right anti-radical,
rSoi(R), is defined for d.g. near-rings with identity, using a construction that
is analogous to that of the (left) socle-ideal, Soi(R). In particular, it is shown
that for finite d.g. near-rings with identity, an ideal A is contained in rSoi(R)
if and only if A \ J2(R) = (0). The relationship between the left and right
socle-ideals is investigated, and it is established that rSoi(R) #18; Soi(R) for
d.g. near-rings with identity and satisfying the descending chain condition for
left R-subgroups.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/2170 |
| Date | 01 March 2007 |
| Creators | Rusznyak, Danielle Sacha |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 386860 bytes, application/pdf |
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