대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제58권6호
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  • Pages.1483-1494
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  • 2021
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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GORENSTEIN FLAT-COTORSION MODULES OVER FORMAL TRIANGULAR MATRIX RINGS

  • Wu, Dejun (Department of Applied Mathematics Lanzhou University of Technology)
  • 투고 : 2020.12.17
  • 심사 : 2021.09.03
  • 발행 : 2021.11.30
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초록

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.

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과제정보

The author would like to thank editorial board and the referee for pertinent comments that improved the exposition.

참고문헌

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