Monomial ideals in polynomial rings

Research Project

Project/Area Number	23540060
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Multi-year Fund
Section	一般
Research Field	Algebra
Research Institution	Meiji University
Principal Investigator	Nakamura Yukio 明治大学, 理工学部, 専任教授 (00308066)
Research Collaborator	Nguen Cong Minh HIGASHIDAIRA Hirotaka KAWAMURA Masaya
Project Period (FY)	2011-04-28 – 2017-03-31
Project Status	Completed (Fiscal Year 2016)
Budget Amount *help	¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000) Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000) Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000) Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000) Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000) Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords	単項式イデアル / Stanley-Reisner 環 / Lefschetz 性 / Cohen-Macaulay / グラフ / 随伴次数環 / 三角圏 / 導来圏 / Stanley-Resner 環 / Lefschetz　性 / quiver / almost split sequence / Buchsbaum 性 / Stanley-Reisner イデアル / 辺イデアル / Ｌｅｆｓｃｈｅｔｚ性 / Ａｒｔｉｎ次数環 / 完全交叉 / regularity / shellable / vertex decomposable / ２部グラフ / sequentially C-M / Cohen-Macaulay 環 / Buchsbaum 環 / k-Buchsbaum 環 / 局所コホモロジー / 被約コホモロジー / マトロイド
Outline of Final Research Achievements	The purpose of the research is to investigate the relation between the property of simplicial complexes in Discrete Mathematics and that of Stanley-Reisner rings in Commutative Algebra. As a result, we characterize the k-Buchsbaum property of the residue class rings of the polynomial ring by the power of Stanley-Reisner ideals.