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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Fields of fractions for group algebras of free groups


Author: Jacques Lewin
Journal: Trans. Amer. Math. Soc. 192 (1974), 339-346
MSC: Primary 16A26
DOI: https://doi.org/10.1090/S0002-9947-1974-0338055-4
MathSciNet review: 0338055
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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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DOI: https://doi.org/10.1090/S0002-9947-1974-0338055-4
Keywords: Free algebras, free group algebras, universal fields of fractions, generalized free products of free groups
Article copyright: © Copyright 1974 American Mathematical Society