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1	Investigation into whether some key properties of BN under addition also apply in BN under multiplication and elaboration of some properties of the smallest ideal of a semigroup Mweete, Kapaipi Hendrix 08 1900 (has links) This dissertation will seek to explore if the properties of some of the key results on semigroups and their compacti cations under the operation of addition also apply under the operation of multiplication. Consider- able emphasis will be placed on the semigroup N of the set of natural numbers and its compacti cation N. Furthermore, the dissertation will discuss the smallest ideal of a semi- group and highlight some of its fundamental properties. / Mathematics / M. Sc. (Mathematics) Semigroup Sub-semigroup Left ideal Right ideal Ideal Minimal left ideal Minimal right ideal Ultrafilter Semigroup compactifcation Commutativity Idempotents Smallest ideal 512.27 Semigroup algebras