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Vietnam Journal of Mathematics 36:3(2008) 261-270

$d$-Koszul Block Modules

Jia - Feng L\``{u}

Abstract. Let $M$ be a weakly $d$-Koszul module and let ${\text{\bf G}}(M)$ be its associated graded module. We give some relations between the minimal projective resolutions of such $M$ and ${\text{\bf G}}(M)$. Moreover, the notion of $d$-Koszul block module} is introduced. For a perfect graded module $M$, we show that $M$ is a $d$-Koszul block module if and only if the Koszul dual $\mathcal{E}(M)=\bigoplus_{i\geq 0}\Ext^i_A(M, A_0)$, is finitely 0-generated as a graded $E(A)=\bigoplus_{i\geq 0}\Ext^i_A(A_0, A_0)$-module.

2000 Mathematics Subject Classification: 16E05, 16E40, 16S37, 16W50.

Keywords: $d$-Koszul algebras, weakly $d$-Koszul modules, $d$-Koszul block modules.