D-Koszul Algebras Over Self-injective Algebras

Let A= A0(?)A1(?) A2 (?)…be a positively Z-graded algebra generated in degrees 0 and 1, where A0 is self-injective. We mainly study the d-Koszul property of A in this thesis, and define the so-called self-injective d-Koszul algebra. More precisely, it is proved that self-injective d-Koszul algebra is d-homogeneous, and its related d-Koszul complex is a minimal graded projective resolution of the trivial A-module A0.We study the structure and property of the Ext-algebra, and prove that the even part Eev(A) of E(A) is a self-injective Koszul algebra and εev(M) is a self-injective Koszul module over Eev(A), where M is a self-injective d-Koszul module over A. Finally, the notion of self-injective d-Koszul algebra/module is generalized to the case of " quasi", and some related properties are studied.