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Two-sided zero product determined algebras
Bajuk, Žan ; Brešar, Matej
Algebra ▫$A$▫ je določena z dvostranskim ničelnim produktom, če za vsak bilinearni funkcional ▫$\varphi: A\times A\to F$▫, ki zadošča ▫$ \varphi(x,y)=0$▫ kadarkoli je ▫$xy=yx=0$▫, obstajata taka ...linearna funkcionala▫ $\tau_1,\tau_2$▫ na ▫$A$▫, da je ▫$\varphi(x,y)=\tau_1(xy) + \tau_2(yx)$▫. Predstavljene so osnovne lastnosti in ekvivalentne definicije, raziskane povezave z lastnostmi odvajanj na teh algebrah, glavni rezultat pa pravi, da je končno-razsežna enostavna algebra, ki ni obseg, določena z dvostrankim ničelnim produktom natanko tedaj, ko je separabilna.
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