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Absolute Valued Algebras

✍ Scribed by Fred B. Wright


Book ID
123669981
Publisher
National Academy of Sciences
Year
1953
Tongue
English
Weight
150 KB
Volume
39
Category
Article
ISSN
0027-8424

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πŸ“œ SIMILAR VOLUMES


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Let A be an absolute valued algebra with involution, in the sense of Urbanik [K. Urbanik, Absolute valued algebras with an involution, Fund. Math. 49 (1961) 247-258]. We prove that A is finite-dimensional if and only if the algebra obtained by symmetrizing the product of A is simple, if and only if

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We prove that if A is a non-associative algebra over the field of real numbers, if 5 5 5 5 5 5 5 5 there is a norm ΠΈ on A satisfying xy s x y for all x, y in A, and if every one-generated subalgebra of A is finite-dimensional, then A is finite-dimensional.