Free group algebras in Malcev–Neumann skew fields of fractions
Free group algebras in Malcev–Neumann skew fields of fractions
Abstract Let K be a skew field and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo>(</m:mo> <m:mi>G</m:mi> <m:mo>,</m:mo> <m:mo><</m:mo> <m:mo>)</m:mo> </m:mrow> </m:math> $(G,&lt;)$ be an ordered group. We show that the skew field generated by the group ring <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>K</m:mi> <m:mo>[</m:mo> <m:mi>G</m:mi> <m:mo>]</m:mo> </m:mrow> </m:math> $K[G]$ inside the Malcev–Neumann series ring <m:math …