摘要
主要给出相对Gorenstein余可解范畴的定义及同调性质,进而研究相对Gorenstein余可解范畴维数及dimgy(M)≤n的若干等价刻画。证明了对任意n≥1,dimgy(M)≤n当且仅当存在正合列0→Gn→Pn-1→…→P1→P0→M→0(其中Pi∈P(A),G∈GPy(A)),当且仅当对任意非负整数t(0≤t≤n),均存在正合列0→Yn→Yn-1→…→Yt→…→Y1→Y0→M→0(其中,Yt∈GPy(A),Yi≠t∈P(A))。
It was gived the definition and properties of relative Gorenstein coresolving category.Moreover it was defined a resolution dimension relative to the relative Gorenstein coresolving category GPy(A),and giveD some equivalent characterizations of dimgy(M)≤n.It was proved that dimgy(M)≤nif and only if exist exact sequence 0→Gn →Pn-1 → … →P1 →P0 →M →0(eachPi ∈P(A),G∈ GPy(A)),if and only if exist exact sequence 0→Yn →Yn-1 → … →Yt → … →Y1 →Y0 → M →0(each Yt ∈ GPy(A),Yi≠t ∈ P(A))for any t(0≤t≤n).
引文
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