English Dictionary

associative algebra

名詞

(algebra) A vector space over some field which also has an associative vector-valued multiplication operator between vectors which together with the abelian group feature of the vector space makes a ring.

日本語の意味

結合代数：ある体上のベクトル空間に、ベクトル間の演算として結合的な（すなわち、(xy)z = x(yz)が成立する）積が定義され、かつそのベクトル空間の加法がアーベル群を成し、加法と積の演算により環の構造を持つ代数的構造。

The researcher studied the representation theory of an associative algebra arising from the quiver.

研究者はクイバーに由来する結合代数の表現論を研究した。

意味（1）

(algebra) A vector space over some field which also has an associative vector-valued multiplication operator between vectors which together with the abelian group feature of the vector space makes a ring.

意味（2）

(algebra) A module over a ring together with an associative bilinear module-element-valued operator between module elements which together with the abelian group feature of the module makes a ring.

associative algebras （ plural ）