Abstract
In this paper we investigate some classes of semigroup rings with respect to (semi)primeness and (semi)primitivity. We do so by extending the techniques developed by Munn in (Proc R Soc Edinbur Sect A 107:175–196, 1987) and (Proc R Soc Edinbur Sect A 115:109–117, 1990) for the study of semigroup rings of inverse semigroups. Restriction, weakly ample and ample semigroups are considered.
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