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设T=(A 0 U B),其中A,B是环,U是左B右A双模.研究了absolutely clean T-模与Gorenstein AC-平坦T-模.在一定条件下,证明了L=(L1,L2)是absolutely clean右T-模,则L1是absolutely clean右A-模且L2是absolutely clean右B-模.作为这个结果的应用,在一定条件下,进一步证明了M=(M1 M2)φM是Gorenstein AC-平坦左T-模当且仅当M1是Gorenstein AC-平坦左A-模,M2/ImφM是Gorenstein AC-平坦左B-模并且φM是单同态.