English Dictionary

algebraic structure

名詞

普遍

(algebra, universal algebra) Any one of the numerous types of mathematical object studied in algebra and especially in universal algebra;

日本語の意味

数学における代数的構造、すなわち、加法や乗法などの演算が定義された集合やその構造を指し、特に普遍代数学で扱われる各種数学的対象の総称

The research paper introduced a new algebraic structure that unifies several known groups and rings under a common framework.

その研究論文は、いくつかの既知の群や環を共通の枠組みの下で統一する新しい代数的構造を紹介した。

意味（1）

(algebra, universal algebra) Any one of the numerous types of mathematical object studied in algebra and especially in universal algebra;

The definition of algebraic structure establishes a framework through which to compare otherwise very different abstract objects, and to study similarities and patterns made apparent by the definition.

意味（2）

(more formally) a mathematical object comprising a carrier set (aka underlying set or domain), an optional scalar set, a set of operations (typically binary operations, but otherwise each of finite arity) and a set of identities (axioms) which the operations must satisfy.

algebraic structures （ plural ）