School of Mathematics
University of the Witwatersrand (Wits), Johannesburg
31 August 2015
Submitted in partial fulflment of a Masters degree at Wits / The operation defined on a discrete semigroup S can be extended to the Stone- Cech compactification
S of S so that for all a 2 S, the left translation S 3 x 7! ax 2 S is continuous, and for all
q 2 S, the right translation S 3 x 7! xq 2 S is continuous. Because any compact right
topological semigroup, S contains a smallest two-sided ideal K( S) which is a completely simple
semigroup. We give an exposition of some basic results related to the semigroup S and to the
semigroup algebra `1( S). In particular, we review the result that `1( N) is semisimple if and only if
`1(K( N)) is semisimple. We also review the reduction of the question whether `1(K( N)) is
semisimple to a question about K( N).
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/19359 |
| Date | 20 January 2016 |
| Creators | Dintoe, Isia T |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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