Finite dimensional zero product determined algebras are generated by idempotents
Brešar, Matej
Algebra $A$ je določena z ničelnim produktom, če za vsako bilinearno preslikavo ▫$f$▫ iz ▫$A \times A$▫ v poljuben vektorski prostor ▫$X$▫ z latnostjo, da iz ▫$xy=0$▫ sledi ▫$f(x,y)=0$▫, obstaja taka ...linearna preslikava ▫$\Phi: A \to X$▫, da je ▫$f(x,y)= \Phi(xy)$▫ za neko linearno preslikavo ▫$\Phi: A \to X$▫. Kot je znano in ni težko videti, je vsaka algebra, ki je generirana z idempotenti, določena z ničelnim produktom. Glavni izrek tega delno preglednega članka pove, da za končno razsežne algebra z enoto velja tudi obratna trditev.
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