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13.
Partial monoid actions and a class of restriction semigroups
Kudryavtseva, Ganna
Obravnavamo razrede lastnih omejitvenih polgrup glede na njihova prirejena parcialna delovanja. Preučujemo močna, antimočna, homomorfna parcialna delovanja, pa tudi tista parcialna delovanja, ki so ...delovanja. Posebej zanimiv je razred, ki je določen s homomorfizmi, predvsem zato ker se elementi tega razreda nahajajo vmes med splošnimi omejitvenimi polgrupami in med poldirektnimi produkti ali . ▫$W$.▫-produkti v vložitveni in pokritveni konstrukciji. Značilno je, da za inverzne polgrupe ta razred nima ustreznega analoga. Definiramo ultra . ▫$F$▫-omejitvene monoide in pokažemo, da so ti monoidi natanko monoidi ▫$Y\ast_mT$▫ iz članka Fountaina, Gomesa in Goulda. Dobimo prezentacijo McAlistera za razred, ki je definiran z dualnimi prehomomorfizmi in vložimo ultra ▫$F$▫-omejitvene monoide, za katere je bazni monoid prost, v ▫$W$▫-produkte polmrež in monoidov. Posledično dobimo nova in enostavnejša dokaza za dva nedavna vložitvena in pokritvena izreka Márie B.Szendrei.
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