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Vietnam Journal of Mathematics 34:3(2006) 341-351  Weakly $d$-Koszul Modules Jia-Feng Lu and Guo-Jun Wang Abstract.  Let A be a d-Koszul algebra and $M\in gr(A)$ we show that $M$ is a weakly $d$-Koszul module if anf only if $\varepsilon(G(M),A_0)= \plus_{n\geq 0}Ext ^{n}_{A(M,A_0)$ is generated in degree 0 as a graded $E(A)$-module. Moreover, relations among weakly $d$-Koszul module,$d$-Koszul modules and Koszul modules are discussed. We also show that the Koszul dual of a weakly $d$-Koszul module $M: \varepsilon(M)= \plus_{n\geq 0}Ext ^{n}_{A(M,A_0)$ is finitely generated as a graded $E(A)$-module.   2000 Mathematics Subject Classification: 16E40, 14E45, 16S37, 16W50. Keywords: $d$-Koszul algebras, $d$-Koszul modules, weakly $d$-Koszul modules.

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