Kania, Tomasz (2017) On bases that are closed under multiplication. American Mathematical Monthly, 124 (7). pp. 651-653. doi:10.4169/amer.math.monthly.124.7.651 ISSN 0002-9890.

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Abstract

It is well known that there is no basis for the field of real numbers regarded as a vector space over any proper subfield that is closed under multiplication. Mabry [3] has extended this result to bases of arbitrary proper field extensions. The aim of this short communication is to notice that the proof of the result concerning the reals may be adjusted to a larger class of algebras (including full matrix algebras); thereby, we subsume Mabry's result.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Varieties (Universal algebra)
Journal or Publication Title:	American Mathematical Monthly
Publisher:	Mathematical Association of America
ISSN:	0002-9890
Official Date:	13 December 2017
Dates:	Date Event 13 December 2017 Published 5 November 2016 Accepted
Volume:	124
Number:	7
Page Range:	pp. 651-653
DOI:	10.4169/amer.math.monthly.124.7.651
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	23 November 2016
Date of first compliant Open Access:	23 November 2016
Funder:	European Research Council (ERC)
Grant number:	Grant Agreement No. 291497
Open Access Version:	ArXiv

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