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The Procesi-Schacher conjecture and Hilbert's 17th problem for algebras with involution
Klep, Igor, matematik ; Unger, Thomas
Leta 1976 sta Procesi in Schacher razvila Artin-Schreierjevo teorijo za centralno enostavne algebre z involucijo. Hkrati sta postavila domnevo, da je v taki algebri element totalno pozitiven natanko ...takrat, ko je vsota hermitskih kvadratov. V tem prispevku podamo protiprimere in študiramo nekatere zglede, kjer domneva drži. Na koncu podamo se Positivstellensatz za nekomutativne polinome, ki so pozitivno semidefinitni na matrikah fiksne velikosti.
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