English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Let  D  be a division ring of fractions of a crossed productF  ⁢   [  G  ,  η  ,  α  ]{F[G,\eta,\alpha]}   , where  F  is a skew field and  G  is a group with Conradian left-order≤{\leq}   . For  D  we introduce the notion of freeness with respect to≤{\leq}    and show that  D  is free in this sense if and only if  D  can canonically be embedded into the endomorphism ring of the right  F -vector spaceF  ⁢   (   (  G  )   ){F((G))}    of all formal power series in  G  over  F  with respect to≤{\leq}   . From this we obtain that all division rings of fractions ofF  ⁢   [  G  ,  η  ,  α  ]{F[G,\eta,\alpha]}    which are free with respect to at least one Conradian left-order of  G  are isomorphic and that they are free with respect to any Conradian left-order of  G . Moreover,F  ⁢   [  G  ,  η  ,  α  ]{F[G,\eta,\alpha]}    possesses a division ring of fraction which is free in this sense if and only if the rational closure ofF  ⁢   [  G  ,  η  ,  α  ]{F[G,\eta,\alpha]}    in the endomorphism ring of the corresponding right  F -vector spaceF  ⁢   (   (  G  )   ){F((G))}    is a skew field.

Free division rings of fractions of crossed products of groups with Conradian left-orders