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An elementary proof of a criterion for linear disjointness
- Source :
- International Journal of Mathematical Education in Science and Technology. 44:614-617
- Publication Year :
- 2013
- Publisher :
- Informa UK Limited, 2013.
-
Abstract
- An elementary proof using matrix theory is given for the following criterion: if F/K and L/K are field extensions, with F and L both contained in a common extension field, then F and L are linearly disjoint over K if (and only if) some K-vector space basis of F is linearly independent over L. The material in this note could serve as enrichment material for the unit on fields in a first course on abstract algebra.
Details
- ISSN :
- 14645211 and 0020739X
- Volume :
- 44
- Database :
- OpenAIRE
- Journal :
- International Journal of Mathematical Education in Science and Technology
- Accession number :
- edsair.doi...........8cd39581c9aef94e7d880fd631bc4dce