• Title/Summary/Keyword: Gorenstein cotorsion dimension

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ON GORENSTEIN COTORSION DIMENSION OVER GF-CLOSED RINGS

  • Gao, Zenghui
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.1
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    • pp.173-187
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    • 2014
  • In this article, we introduce and study the Gorenstein cotorsion dimension of modules and rings. It is shown that this dimension has nice properties when the ring in question is left GF-closed. The relations between the Gorenstein cotorsion dimension and other homological dimensions are discussed. Finally, we give some new characterizations of weak Gorenstein global dimension of coherent rings in terms of Gorenstein cotorsion modules.

GORENSTEIN FLAT-COTORSION MODULES OVER FORMAL TRIANGULAR MATRIX RINGS

  • Wu, Dejun
    • Bulletin of the Korean Mathematical Society
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    • v.58 no.6
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    • pp.1483-1494
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    • 2021
  • 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.