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http://dx.doi.org/10.4134/BKMS.b201049

GORENSTEIN FLAT-COTORSION MODULES OVER FORMAL TRIANGULAR MATRIX RINGS  

Wu, Dejun (Department of Applied Mathematics Lanzhou University of Technology)
Publication Information
Bulletin of the Korean Mathematical Society / v.58, no.6, 2021 , pp. 1483-1494 More about this Journal
Abstract
Let A and B be rings and U be a (B, A)-bimodule. If BU has finite flat dimension, UA has finite flat dimension and U ⊗A 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=\(\array{A&0\\U&B}\)$ 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;
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