Simple algebra

English

Noun

1. Template:Lb An Template:L that contains no nontrivial Template:L (two-sided) Template:L and whose multiplication operation is not zero (i.e., there exist a and b such that ab ≠ 0).
   • 1945 [McGraw-Hill], Template:W, 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 $A$ is a finite dimensional simple algebra over $F$, then $A\cong M_n(\mathrm{\Delta })$ where $\mathrm{\Delta }$ is a finite dimensional division algebra over $\mathrm{\Delta }$.Template:Sic

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Hyponyms

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Translations

• Italian: Template:T

See also

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Further reading

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