Gorenstein flat modules and dimensions over formal triangular matrix rings
L Mao - Journal of Pure and Applied Algebra, 2020 - Elsevier
Abstract Let T=(A 0 UB) be a formal triangular matrix ring, where A and B are rings and U is
a (B, A)-bimodule. We prove that, if T is a right coherent ring, UB has finite flat dimension, UA
has finite flat or injective dimension, then a left T-module (M 1 M 2) φ M is Gorenstein flat if
and only if M 1 is a Gorenstein flat left A-module, M 2/im (φ M) is a Gorenstein flat left B-
module and the morphism φ M: U⊗ AM 1→ M 2 is a monomorphism. This result extends an
earlier result in this direction. In addition, we give an estimate of Gorenstein flat dimension of …
a (B, A)-bimodule. We prove that, if T is a right coherent ring, UB has finite flat dimension, UA
has finite flat or injective dimension, then a left T-module (M 1 M 2) φ M is Gorenstein flat if
and only if M 1 is a Gorenstein flat left A-module, M 2/im (φ M) is a Gorenstein flat left B-
module and the morphism φ M: U⊗ AM 1→ M 2 is a monomorphism. This result extends an
earlier result in this direction. In addition, we give an estimate of Gorenstein flat dimension of …
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