Some Related Studies On (Generalized-)(ρ,λ)-Koszul Algebras(Modules)

Note that Koszul algebras, d-Koszul algebras and piecewise-Koszul algebras all have only one "jump-degree", in order to breakthrough this restrict, Lu and Zhao intro-duced the notion of (ρ,λ)-Koszul algebra in2010, which include Koszul and d-Koszul algebras and has any finite jump-degrees. The present thesis is a continuous work on of (ρ,λ)-Koszul algebras which is arranged as follows:In chapter1, we describe the purpose of this paper, the main results, prior knowl-edge and so on;In chapter2, firstly, we prove that under a special graded Morita equivalence, the (ρ,λ)-Koszulity is an invariance. Secondly, Green et al studied the relationship between the category of Koszul modules and the category of modules with linear presentations. Inspired, by their results, we give some necessary and sufficient conditions for the category of (ρ,λ)-Koszul modules to coincide with the category of modules with linear presentations.In chapter3, we extend (ρ,λ)-Koszul objects to the non-pure case, define generalized-(ρ,λ)-Koszul objects. Moreover, some basic properties and criteria of generalized-(ρ,λ)-Koszul algebras (modules) are given.