Free group algebras in Malcev-Neumann skew fields of fractions
Javier S\'anchez
TL;DR
This paper demonstrates that within the Malcev-Neumann series ring constructed from an ordered group, the skew field generated by the group ring contains noncommutative free group algebras, revealing new algebraic structures.
Contribution
It establishes the existence of noncommutative free group algebras inside skew fields generated by group rings in Malcev-Neumann series rings.
Findings
Contains noncommutative free group algebras
Shows the structure within Malcev-Neumann series rings
Extends understanding of skew field algebraic properties
Abstract
Let K be a skew field and (G,<) an ordered group. We show that the skew field generated by the group ring K[G] inside the Malcev-Neumann series ring K((G;<)) contains noncommutative free group algebras.
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