Weakly Koszul-Like Modules

作者：Chen, Pei-Sen; Lu, Jia-Feng

来源：Mathematical Notes, 2012, 91(1-2): 105-127.

DOI：10.1134/S0001434612010117

• Koszul-like algebras
• Koszul-like modules
• weakly Koszul-like modules

The Koszul-like property for any finitely generated graded modules over a Koszul-like algebra is investigated and the notion of weakly Koszul-like module is introduced. We show that a finitely generated graded module M is a weakly Koszul-like module if and only if it can be approximated by Koszul-like graded submodules, which is equivalent to the fact that G(M) is a Koszul-like module, where G(M) denotes the associated graded module of M. As applications, the relationships between minimal graded projective resolutions of M and G(M), and Koszul-like submodules are established. Moreover, the Koszul dual of a weakly Koszul-like module is proved to be generated in degree 0 as a graded E(A)-module.

• 出版日期2012-2
• 单位浙江师范大学