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.References
- Gilbert Baumslag, Positive one-relator groups, Trans. Amer. Math. Soc. 156 (1971), 165–183. MR 274562, DOI 10.1090/S0002-9947-1971-0274562-8
- P. M. Cohn, Free ideal rings, J. Algebra 1 (1964), 47–69. MR 161891, DOI 10.1016/0021-8693(64)90007-9
- P. M. Cohn, Free rings and their relations, London Mathematical Society Monographs, No. 2, Academic Press, London-New York, 1971. MR 0371938
- M. J. Dunwoody, Relation modules, Bull. London Math. Soc. 4 (1972), 151–155. MR 327915, DOI 10.1112/blms/4.2.151
- Ian Hughes, Division rings of fractions for group rings, Comm. Pure Appl. Math. 23 (1970), 181–188. MR 263934, DOI 10.1002/cpa.3160230205
- Abraham Karrass and Donald Solitar, On finitely generated subgroups of a free group, Proc. Amer. Math. Soc. 22 (1969), 209–213. MR 245655, DOI 10.1090/S0002-9939-1969-0245655-2
- A. Karrass and D. Solitar, The subgroups of a free product of two groups with an amalgamated subgroup, Trans. Amer. Math. Soc. 150 (1970), 227–255. MR 260879, DOI 10.1090/S0002-9947-1970-0260879-9
- Abraham A. Klein, Involutorial division rings with arbitrary centers, Proc. Amer. Math. Soc. 34 (1972), 38–42. MR 304425, DOI 10.1090/S0002-9939-1972-0304425-7
- Jacques Lewin, A note on zero divisors in group-rings, Proc. Amer. Math. Soc. 31 (1972), 357–359. MR 292957, DOI 10.1090/S0002-9939-1972-0292957-X
- B. H. Neumann, On ordered division rings, Trans. Amer. Math. Soc. 66 (1949), 202–252. MR 32593, DOI 10.1090/S0002-9947-1949-0032593-5
Additional Information
- © Copyright 1974 American Mathematical Society
- 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