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13.
Associativity of the ▫$\nabla$▫-operation on bands in rings
Cvetko-Vah, Karin ; Leech, Jonathan
Naj bo ▫$S$▫ multiplikativni pas idempotentov v kolobarju ▫$R$▫. Če sta ▫$e$▫ in ▫$f$▫ iz ▫$S$▫ idempotenta, je njun ▫$\nabla$▫-produkt ▫$e\nabla f = e+f+fe-efe-fef$▫ spet idempotent in leži nad ...▫$e$▫ in ▫$f$▫ v ▫$R$▫, kakor ležita ▫$ef$▫ in ▫$fe$▫ pod ▫$e$▫ in ▫$f$▫. V tem članku preučujemo ▫$\nabla$▫-pasove v kolobarjih, to je pasove v kolobarjih, ki so zaprti za operacijo ▫$\nabla$▫. Podamo vrsto različnih kriterijev za asociativnost te operacije. Obravnavamo tudi vprašanje, kdaj dani pas ▫$S$▫ v ▫$R$▫ generira ▫$\nabla$▫-pas.
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