三角矩阵余代数上的有限Gorenstein余表现余模

Finitely Gorenstein copresented comodules over triangular matrix coalgebras

利用范畴的等价定理和范畴之间的正合函子,给出了三角矩阵余代数■上的有限Gorenstein余表现余模的具体形式,并且得到三角矩阵余代数Γ与余代数T及U之间的有限Gorenstein余表现维数的关系Max{G.cp.dimT,G.cp.dimU}≤G.cp.dimΓ≤G.cp.dimT+G.cp.dimU+1。

The specific form of the finitely Gorenstein copresented comodule over a triangular matrix coalgebra ■ 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.