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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Acknowledgments
The authors wish to thank Victoria Gould for drawing their attention to the class of restriction semigroups with an inverse skeleton; Mikhail Volkov for having translated into English the proof of Domanov’s theorem, published in Russian; Mária Szendrei and João Araújo for some fruitful conversations; and the referee for helpful comments and suggestions. This work was partially supported by FCT’s project PEst-OE/MAT/UI0143/2013–14 and was developed within the activities of the Centro de Álgebra da Universidade de Lisboa.
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Communicated by Mark V. Lawson.
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Gomes, G.M.S., Santa-Clara, C. & Soares, F. The semigroup ring of a restriction semigroup with an inverse skeleton. Semigroup Forum 90, 449–474 (2015). https://doi.org/10.1007/s00233-014-9612-1
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DOI: https://doi.org/10.1007/s00233-014-9612-1