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

Canadian mathematical bulletin

关键词: $*$--orderings;    valuations;    rings with involution;   

DOI  :  10.4153/CMB-2007-010-4

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We study natural $*$-valuations, $*$-places and graded $*$-ringsassociated with $*$-ordered rings.We prove that the natural $*$-valuation is always quasi-Ore and iseven quasi-commutative (emph{i.e.,} the corresponding graded $*$-ring iscommutative), provided the ring contains an imaginary unit.Furthermore, it is proved that the graded $*$-ring is isomorphicto a twisted semigroup algebra. Our results are applied to answer a questionof Cimpriv c regarding $*$-orderability of quantumgroups.

【 授权许可】

Unknown