Geodesic
On Valuations, Places and Graded Rings Associated to ∗-Orderings
Canadian mathematical bulletin, Tome 50 (2007) no. 1, pp. 105-112

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DOI

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 Cimprič regarding $*$ -orderability of quantum groups.
DOI : 10.4153/CMB-2007-010-4
Mots-clés : 14P10, 16S30, 16W10, ∗-orderings, valuations, rings with involution 
Klep, Igor. On Valuations, Places and Graded Rings Associated to ∗-Orderings. Canadian mathematical bulletin, Tome 50 (2007) no. 1, pp. 105-112. doi: 10.4153/CMB-2007-010-4
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     title = {On {Valuations,} {Places} and {Graded} {Rings} {Associated} to {\ensuremath{*}-Orderings}},
     journal = {Canadian mathematical bulletin},
     pages = {105--112},
     year = {2007},
     volume = {50},
     number = {1},
     doi = {10.4153/CMB-2007-010-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-010-4/}
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