Gorenstein flat-cotorsion modules over formal triangular matrix rings
Bull. Korean Math. Soc. 2021 Vol. 58, No. 6, 1483-1494
Published online November 1, 2021
Printed November 30, 2021
Dejun Wu
Lanzhou University of Technology
Abstract : Let $A$ and $B$ be rings and $U$ be a $(B,A)$-bimodule. If $_BU$ has finite flat dimension, $U_A$ has finite flat dimension and $\tpa{U}{C}$ is a cotorsion left $B$-module for any cotorsion left $A$-module $C$, then the Gorenstein flat-cotorsion modules over the formal triangular matrix ring $T=\left(\begin{smallmatrix} A & 0 \\ U & B \\ \end{smallmatrix}\right)$ are explicitly described. As an application, it is proven that each Gorenstein flat-cotorsion left $T$-module is flat-cotorsion if and only if every Gorenstein flat-cotorsion left $A$-module and $B$-module is flat-cotorsion. In addition, Gorenstein flat-cotorsion dimensions over the formal triangular matrix ring $T$ are studied.
Keywords : Formal triangular matrix ring, Gorenstein flat-cotorsion module
MSC numbers : 16E10, 16G50, 18G25
Supported by : The author was partly supported by NSF of China grants 11761047 and 11861043.
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