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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An extension of Dedekind's linear independence theorem


Author: Charles M. Walters
Journal: Proc. Amer. Math. Soc. 39 (1973), 73-76
MSC: Primary 12H05
MathSciNet review: 0311632
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Abstract: Dedekind's theorem on the linear independence of isomorphisms of a field is extended to the case of linear independence of compositions of isomorphisms and powers of a derivation, $ D$, for fields of characteristic zero which contain an element $ s$ such that $ D(s) = 1$.


References [Enhancements On Off] (What's this?)

  • [1] Nathan Jacobson, Lectures in abstract algebra. Vol III: Theory of fields and Galois theory, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London-New York, 1964. MR 0172871 (30 #3087)
  • [2] C. M. Walters, Continuous linear transformations on the field of Mikusiński operators, Ph.D. Thesis, North Carolina State University, Raleigh, N.C., 1971.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0311632-7
PII: S 0002-9939(1973)0311632-7
Keywords: Derivation, linearly independent
Article copyright: © Copyright 1973 American Mathematical Society