simple algebra

短语

[计] 单代数

词形变化

simple algebras 复数 simple algebras

释义与例句

n.
  1. 1.

    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).

    数学

    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 A is a finite dimensional simple algebra over F, then A≅M_n(Δ) where Δ is a finite dimensional division algebra over Δ.