Abstract
AbstractWe 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 Cimprič regarding ∗-orderability of quantum groups.
Publisher
Canadian Mathematical Society
Cited by
5 articles.
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1. Residually *-Abelian Valuation with Residue Characteristic Not 2;Communications in Algebra;2014-03-13
2. Residually *-Abelian Valuation;Communications in Algebra;2013-09-02
3. *-orderable semigroups;Semigroup Forum;2009-10-27
4. The Joly–Becker theorem for *–orderings;Annales de la Faculté des sciences de Toulouse : Mathématiques;2008-12-04
5. Embedding ∗-ordered domains into skew fields;Journal of Algebra;2006-09