Journal of the
Korean Mathematical Society JKMS

Let $\Gamma$ be a Gorenstein coalgebra over a filed $k$. We introduce the Gorenstein transpose via a minimal Gorenstein injective copresentation of a quasi-finite $\Gamma$-comodule, and obtain a relation between a Gorenstein transpose of a quasi-finite comodule and a transpose of the same comodule. As an application, we obtain that the almost split sequences are constructed in terms of Gorenstein transpose.

Keywords: Gorenstein coalgebra, Gorenstein injective comodule, transpose, almost split sequence

MSC numbers: 16T15, 18G25, 16G70

Supported by: This work was financially supported by National Natural Science Foundation of China (Grant No. 11671126, 12071120).