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Induced liftings, exchange rings and semi-perfect algebras
Pavešić, Petar
Mnoge pomembne razrede kolobarjev je možno opredeliti z uporabo lastnosti dviganja idempotentov vzdolž idealov določenega tipa: klasični primeri so polperfektni kolobarji, polregularni kolobarji in ...izmenljivi kolobarji. Delo začnemo z obravnavo nekaterih razširitev pojma dviganja idealov in posplošitvijo nekaterih klasičnih izrekov o dvigu. Nato opišemo metodo induciranih dvigov, ki omogoča prenos dvigov s kolobarja na njegove podkolobarje. S pomočjo te metode izpeljemo pogoje, pri katerih je podkolobar izmenljivega kolobarja prav tako izmenljiv ter dokažemo, da je končna algebra nad komutativnim lokalnim kolobarjem polperfektna, kakor hitro jo je mogoče primerno upodobiti v nek izmenljivi kolobar.
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