We study various quotient maps between frames which are defined by stipulating that they
satisfy certain conditions on the cozero parts of their domains and codomains. By way of
example, we mention that C-quotient and C -quotient maps (as defined by Ball and Walters-
Wayland [7]) are typical of the types of homomorphisms we consider in the initial parts of the
thesis. To be little more precise, we study uplifting quotient maps, C1- and C2-quotient maps
and show that these quotient maps possess some properties akin to those of a C-quotient
maps. The study also focuses on R - and G - quotient maps and show, amongst other
things, that these quotient maps coincide with the well known C - quotient maps in mildly
normal frames. We also study quasi-F frames and give a ring-theoretic characterization
that L is quasi-F precisely when the ring RL is quasi-B´ezout. We also show that quasi-F
frames are preserved and reflected by dense coz-onto R -quotient maps. We characterize
normality and some of its weaker forms in terms of some of these quotient maps. Normality
is characterized in terms of uplifting quotient maps, -normally separated frames in terms
of C1-quotient maps and mild normality in terms of R - and G -quotient maps. Finally we
define cozero complemented frames and show that they are preserved and reflected by dense
z#- quotient maps. We end by giving ring-theoretic characterizations of these frames. / Mathematical Science / D. Phil. (Mathematics)
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:unisa/oai:umkn-dsp01.int.unisa.ac.za:10500/6050 |
| Date | 02 1900 |
| Creators | Matlabyana, Mack Zakaria |
| Contributors | Dube, T. A. |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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