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No nontrivial Hamel basis is closed under multiplication

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Summary.

If H is a Hamel basis for a field \( {\user2{\mathbb{F}}} \) over a proper subfield of \( {\user2{\mathbb{F}}}, \) then H cannot be closed under the taking of products.

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Authors and Affiliations

  1. Department of Mathematics, Louisiana State University in Shreveport, Shreveport, LA, 71115-2399, USA

    Richard D. Mabry

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  1. Richard D. Mabry
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Correspondence to Richard D. Mabry.

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Manuscript received: September 1, 2004 and, in final form, February 19, 2005.

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Mabry, R.D. No nontrivial Hamel basis is closed under multiplication. Aequ. math. 71, 294–299 (2006). https://doi.org/10.1007/s00010-005-2804-8

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  • DOI: https://doi.org/10.1007/s00010-005-2804-8

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