The lower and upper bounds of the degree distribution of a graded algebra  

作　　者：SI JunRu 

机构地区：[1]Department of Mathematics,Hangzhou Dianzi University

出　　处：《Science China Mathematics》2013年第5期983-994,共12页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11026106 and 10971188);National Natural Science Foundation of Zhejiang Province of China(Grant No.LQ12A01028)

摘　　要：For a graded algebra,the minimal projective resolution often reveals amounts of information.All generated degrees of modules in the minimal resolution of the trivial module form a sequence,which can be called the degree distribution of the algebra.We try to find lower and upper bounds of the degree distribution,introduce the notion of(s,t)-(homogeneous) determined algebras and construct such algebras with the aid of algebras with pure resolutions.In some cases,the Ext-algebra of an(s,t)-(homogeneous) determined algebra is finitely generated.For a graded algebra, the minimal projective resolution often reveals amounts of information. All generated degrees of modules in the minimal resolution of the trivial module form a sequence, which can be called the degree distribution of the algebra. We try to find lower and upper bounds of the degree distribution, introduce the notion of （s,t）-（homogeneous） determined algebras and construct such algebras with the aid of algebras with pure resolutions. In some cases, the Ext-algebra of an （s, t）-（homogeneous） determined algebra is finitely generated.

关 键 词：d-Koszul algebra spectral sequence regular normal extension 

分 类 号：O153[理学—数学]