弱分段Koszul模(英文)

Weakly Piecewise-Koszul Modules

任意一个弱分段Koszul模M都被证明存在一个自然的分次子模链0=U_0(?)U_1(?)U_2(?)…(?) U_t=M使得每个商U_i/U_(i-1)都是分段Koszul模.本文的主要目的是建立M和U_i/U_(i-1)的极小分次投射解之间的关系.对n≥0,证明了P_n=⊕_(i=1)~t P_n^i,其中P_*~i→U_i/U_(i-1)→0和P_*→M→0是相应的极小分次投射解,作为其直接推论,有pd(M)=max{pd(U_i/U_(i-1))}成立.

It has been proved that for a weakly piecewise-Koszul module M, there is a natural filtration of graded submodules 0 = Uo C_ U1 C U2 C ... CUt = M such that all quotients Ui/Ui-1 are piecewise-Koszul. The main aim of this paper is to establish the relationship of the minimal graded projective resolutions of M and these quotients Ui/Ui-1. t i More precisely, we obtain Pn ≌ ＋i^t i=1 Pn^i for all n 〉 0, where 7v,i -4 Ui/Ui-1 -4 0 and P, -4-4 M -4 0 are the corresponding minimal graded projective resolutions, which implies easily that pd（M） = max{pd（Ui/Ui-1）}.