English Dictionary

combinatorial commutative algebra

名詞

不可算名詞

(algebra) A relatively new discipline in mathematics that combines techniques and concepts from combinatorics and commutative algebra, and in which the geometry of convex polytopes also plays a significant role.

日本語の意味

数学の分野の一つで、組み合わせ論と可換代数学の手法や概念を融合し、凸多面体の幾何学的性質なども考慮して研究を行う新しい分野

Recent advances in combinatorial commutative algebra have clarified the connections between monomial ideals and the geometry of polytopes.

最近の組合せ可換代数の進展は、モノミアルイデアルと多面体の幾何学との関係を明らかにした。

意味（1）

(algebra) A relatively new discipline in mathematics that combines techniques and concepts from combinatorics and commutative algebra, and in which the geometry of convex polytopes also plays a significant role.

This construction has become a fundamental tool in combinatorial commutative algebra due to the work of Stanley, Hochster and Reisner ([Ho77], [S75], [S96], [R76]).