ERIC Number: EJ1013299
Record Type: Journal
Publication Date: 2013
Abstractor: As Provided
Reference Count: 7
An Elementary Proof of a Criterion for Linear Disjointness
Dobbs, David E.
International Journal of Mathematical Education in Science and Technology, v44 n4 p614-617 2013
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.
Descriptors: Mathematical Logic, Validity, Algebra, Matrices, Mathematics Instruction, College Mathematics
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Publication Type: Reports - Descriptive; Journal Articles
Education Level: Higher Education; Postsecondary Education
Authoring Institution: N/A