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A Normal Form in Free Fields

Published online by Cambridge University Press:  20 November 2018

Paul M. Cohn  and
Christophe Reutenauer
Paul M. Cohn
Affiliation:
Department of Mathematics University College London Gower Street London WC1E6BT United Kingdom
Christophe Reutenauer
Affiliation:
Mathématiques-Informatique UQAM C.P. 8888 Suce. A Montréal, Québec H3C3P8
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Abstract

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We give a normal form for the elements in the free field, following the lines of the minimization theory of noncommutative rational series.

Keywords

12E15
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 3 , 01 June 1994 , pp. 517 - 531
Copyright
Copyright © Canadian Mathematical Society 1994

References

[A] Amitsur, S. A., Rational identities and applications to algebra and geometry, J. Algebra 3(1966), 304–359.Google Scholar
[BR] Berstel, J. and Reutenauer, C., Rational series and their languages. Springer-Verlag, 1988.Google Scholar
[Cl] Cohn, P. M., Free rings and their relations, Acad. Press, 1985 (first edition 1971).Google Scholar
[C2] Cohn, P. M., Skew field constructions, Cambridge Univ. Press, London Math. Soc. Lect. Notes (27), 1977.Google Scholar
[C3] Cohn, P. M., The universal field of fractions of a semifir I. Numerators and Denominators, Proc. London Math Soc. 44(1982), 1–32.Google Scholar
[E] Eilenberg, S., Automata, languages and machines, Vol. A, Acad. Press, 1974.Google Scholar
[F] Fliess, M., Matrices de Hankel, J. Math. Pures Appl. 53(1974), 197–222.Google Scholar
[J] Jacob, G., Représentations et substitutions matricielles dans la théorie algébrique des transductions, Thèse Se. Maths, Univ. Paris 7, 1975.Google Scholar
[L] Lewin, J., Fields offractions for group algebras of free groups, Trans. Amer. Math. Soc. 192(1974), 339–346.Google Scholar
[R] Roberts, M. L., Endomorphism rings of finitely presented modules over free algebras, J. London Math. Soc. 30(1984), 197–209.Google Scholar
[SS] Salomaa, A. and Soittola, M., Automata-theoretic aspects of formal power series, Springer-Verlag, 1978.Google Scholar
[SI] Schutzenberger, M.-R., On the definition of a family of automata, Inform, and Control 4(1961), 245–270.Google Scholar
[S2] Schutzenberger, M.-R., On a theorem ofJungen, Proc. Amer. Math. Soc. 13(1962), 885–890.Google Scholar