关键词: 三角矩阵余代数, 有限Gorenstein余表现余模, 有限Gorenstein余表现维数

Abstract: The specific form of the finitely Gorenstein copresented comodule over a triangular matrix coalgebra Γ=(T _TM_U0 U)is given by the equivalence theorem of categories and the exact functors between categories, and a relationship between the finitely Gorenstein copresented dimensions of the triangular matrix coalgebra Γ and coalgebras T and U is obtained as follows Max{G.cp.dimT,G.cp.dimU}≤G.cp.dimΓ≤G.cp.diimT+G.cp.dimU+1.

Key words: triangular matrix coalgebra, finitely Gorenstein copresented comodule, finitely Gorenstein co-presented dimension