English Dictionary

simple algebra

名詞

(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).

日本語の意味

非自明な両側イデアル（単なる零イデアルと全体以外のイデアルを持たず）、かつその積が零にならない代数。

The classification of modules over a simple algebra often reveals deep structural insights about representation theory.

単純代数上の加群の分類は、しばしば表現論に関する深い構造的洞察を明らかにする。

意味（1）

(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).

A semi-simple algebra over F is either simple or the direct sum of simple algebras over F.

simple algebras （ plural ）