JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (10): 44-49.doi: 10.6040/j.issn.1671-9352.0.2021.723

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n-Gorenstein projective modules over formal triangular matrix rings

NIU Shao-hua, YANG Gang   

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Published:2022-10-06

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Abstract: Let n be an integer, T=(A 0U B) a formal triangular matrix ring, where A and B are rings and U is a (B,A)-bimodule, BU is projective, UA has finite flat dimension. It is proved that, if a left T-module (M1M2)φM is n-Gorenstein projective, then M1 is (n-1)-Gorenstein projective in A-Mod, M2/Im(φM)is n-Gorenstein projective in B-Mod, and φM:U⊗AM1→M2 is a monomorphism. Conversely, if M1 is n-Gorenstein projective in A-Mod, M2/Im(φM) is n-Gorenstein projective in B-Mod, and φM:U⊗AM1→M2 is a monomorphism, then the left T-module (M1M2)φM is n-Gorenstein projective.

Key words: n-Gorenstein projective module, formal triangular matrix ring, adjoint pair

CLC Number: 

  • O154.2
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