On Valuations, Places and Graded Rings Associated to *-Orderings

• Autores: Igor Klep
• Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 50, Nº 1, 2007, págs. 105-112
• Idioma: inglés
• DOI: 10.4153/cmb-2007-010-4
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• Resumen

  • We study natural *-valuations, *-places and graded *-rings associated with *-ordered rings. We prove that the natural *-valuation is always quasi-Ore and is even quasi-commutative (i.e., the corresponding graded *-ring is commutative), provided the ring contains an imaginary unit. Furthermore, it is proved that the graded *-ring is isomorphic to a twisted semigroup algebra. Our results are applied to answer a question of Cimpric regarding *-orderability of quantum groups