On a question of Makar-Limanov
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- by Zinovy Reichstein PDF
- Proc. Amer. Math. Soc. 124 (1996), 17-19 Request permission
Abstract:
Let $K$ be an uncountable field, let $K \subset F$ be a field extension, and let $A$ be an associative $K$-algebra. We show that if $F \otimes _K A$ contains a non-commutative free algebra, then so does $A$.References
- L. Makar-Limanov, On free subsemigroups of skew fields, Proc. Amer. Math. Soc. 91 (1984), no. 2, 189–191. MR 740167, DOI 10.1090/S0002-9939-1984-0740167-X
- —, On free subobjects of skew fields, Methods in Ring Theory (F. van Oystaeyen, ed.), NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., vol. 233, Reidel, Dordrecht, 1984, pp. 281–285.
- L. Makar-Limanov and P. Malcolmson, Free subalgebras of enveloping fields, Proc. Amer. Math. Soc. 111 (1991), no. 2, 315–322. MR 1041015, DOI 10.1090/S0002-9939-1991-1041015-7
- A. A. Klein, Free subsemigroups of domains, Proc. Amer. Math. Soc. 116 (1992), no. 2, 339–341. MR 1096212, DOI 10.1090/S0002-9939-1992-1096212-2
Additional Information
- Zinovy Reichstein
- Affiliation: Department of Mathematics, Oregon State University, Corvallis, Oregon 97331
- MR Author ID: 268803
- Email: zinovy@math.orst.edu
- Received by editor(s): April 11, 1994
- Received by editor(s) in revised form: June 24, 1994
- Communicated by: Ken Goodearl
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 17-19
- MSC (1991): Primary 16S10; Secondary 20M05
- DOI: https://doi.org/10.1090/S0002-9939-96-03014-6
- MathSciNet review: 1286005