simple algebra
English
Noun
simple algebra (plural simple algebras)
- (algebra) An algebra that contains no nontrivial proper (two-sided) ideals and whose multiplication operation is not zero (i.e., there exist a and b such that ab ≠ 0).
- 1945 [McGraw-Hill], E. T. Bell, 2nd Edition, 1992, Dover, The Development of Mathematics, page 252,
- A semi-simple algebra over F is either simple or the direct sum of simple algebras over F.
- 1989 [W. H Freeman & Company], Nathan Jacobson, Basic Algebra II, 2nd Edition, 2009, Dover, page 215,
- If is a finite dimensional simple algebra over , then where is a finite dimensional division algebra over .[sic]
- 2005, Miles Reid (translator), Igor R. Shafarevich, Basic Notions of Algebra, Springer, page 198,
- One proves that if is a simple algebra over , then is either a simple algebra over , or a direct sum of two isomorphic simple algebras. Thus the problem of studying simple algebras over reduces to a similar problem over .
- 1945 [McGraw-Hill], E. T. Bell, 2nd Edition, 1992, Dover, The Development of Mathematics, page 252,
Translations
algebra that contains no nontrivial proper ideals and whose multiplication operation is not zero
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See also
- semisimple algebra
Further reading
Central simple algebra on Wikipedia.Wikipedia Semisimple algebra on Wikipedia.Wikipedia
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