JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (8): 33-37.doi: 10.6040/j.issn.1671-9352.0.2022.634

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Construction of Gorenstein projective modules over tensor rings

Guoliang TANG()   

  1. School of Mathematics and Statistics, Kashi University, Kashi 844008, Xinjiang, China
  • Received:2022-11-24 Online:2023-08-20 Published:2023-07-28

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Abstract:

Let R be any ring, M a nilpotent R-bimodule, TR(M) is the associated tensor ring. Suppose that ExtR1(G, M⊗Ri⊗RP)=0=Tor1R(M, M⊗Ri⊗RG), where P is a projective R-module, G is a Gorenstein projective R-module, and i≥0. It is proved that a TR(M)-module: (X, u) is a Gorenstein projective TR(M)-module if u is a monomorphism and the cokernel of u is a Gorenstein projective R-module.

Key words: tensor rings, Gorenstein projective modules

CLC Number: 

  • O154.2
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