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▫$n$▫-real valuations and the higher level version of the Krull-Baer theorem
Klep, Igor, matematik ; Velušček, Dejan
Cimprič je v [Comm. Algebra 29 (2001) 193-201] za vsak ▫$m \in \mathbb N$▫ podal primere nekomutativnih obsegov, ki vsebujejo ureditve reda ▫$2m$▫, a ne vsebujejo nobene ureditve reda ▫$m$▫. V članku ...podamo bistveno poenostavljene primere in raziščemo ta pojav s pomočjo teorije valuacij. Definirano skoraj realne in ▫$n$▫-realne valuacije in obravnavamo dvige ureditev iz residualnih obsegov v originalni nekomutativni obseg. Za razliko od komutativne teorije, taki dvigi niso zmeraj mogoči, v članku pa podamo potrebne in zadostne pogoje za njihov obstoj. Dokažemo še ustrezno posplošitev Krull-Baerovega izreka. V zadnjem razdelku uporabimo prej razvito teorijo in primere za odgovor na vprašanje, ki sta ga zastavila Marshall in Zhang [J. Algebra 212 (1) (1999) 190-207].
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