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

摘要

This dissertation will seek to explore if the properties of some of the keyresults on semigroups and their compacti cations under the operationof addition also apply under the operation of multiplication. Consider-able emphasis will be placed on the semigroup N of the set of naturalnumbers and its compacti cation N.Furthermore, the dissertation will discuss the smallest ideal of a semi-group and highlight some of its fundamental properties.