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On a question ofMakar-Limanov

Author: Zinovy Reichstein
Journal: Proc. Amer. Math. Soc. 124 (1996), 17-19
MSC (1991): Primary 16S10; Secondary 20M05
MathSciNet review: 1286005
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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 [Enhancements On Off] (What's this?)

  • L1 L. Makar-Limanov, On free subsemigroups of skew fields, Proc. Amer. Math. Soc. 91 (1984), 189--191.MR 85j:16022
  • L2 ------, 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. CMP 17:06
  • LM L. Makar-Limanov and P. Malcolmson, Free subalgebras of enveloping fields, Proc. Amer. Math. Soc. 111 (1991), 315--322. MR 91f:16023
  • K A. A. Klein, Free subsemigroups of domains, Proc. Amer. Math. Soc. 116 (1992), 339--341.MR 92m:16045

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Additional Information

Zinovy Reichstein
Affiliation: Department of Mathematics, Oregon State University, Corvallis, Oregon 97331

Received by editor(s): April 11, 1994
Received by editor(s) in revised form: June 24, 1994
Communicated by: Ken Goodearl
Article copyright: © Copyright 1996 American Mathematical Society

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