Fields of fractions for group algebras of free groups

Lewin, Jacques

doi:10.1090/S0002-9947-1974-0338055-4

Fields of fractions for group algebras of free groups
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by Jacques Lewin PDF

Trans. Amer. Math. Soc. 192 (1974), 339-346 Request permission

Abstract:

Let KF be the group algebra over the commutative field K of the free group F. It is proved that the field generated by KF in any Mal’cev-Neumann embedding for KF is the universal field of fractions $U(KF)$ of KF. Some consequences are noted. An example is constructed of an embedding $KF \subset D$ into a field D with $D\;\not \simeq \;U(KF)$. It is also proved that the generalized free product of two free groups can be embedded in a field.

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