Gorenstein Hereditary and $FP$-Injectivity over Formal Triangular Matrix Rings
Received:November 19, 2019  Revised:August 01, 2020
Key Word: Gorenstein (semihereditary) hereditary   formal triangular matrix ring   $FP$-injective module   $n$-$FC$ ring  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11671126).
Author NameAffiliation
Meiqi YAN School of Mathematics, Faculty of Science, Beijing University of Technology, Beijing 100124, P. R. China 
Hailou YAO School of Mathematics, Faculty of Science, Beijing University of Technology, Beijing 100124, P. R. China 
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Abstract:
      In this paper we study Gorenstein (semiheredity) heredity, finite presentedness and $FP$-injectivity of modules over a formal triangular matrix ring. We provide necessary and sufficient conditions for such rings to be Gorenstein (semihereditary) hereditary and investigate when a triangular matrix ring is an $n$-$FC$ ring.
Citation:
DOI:10.3770/j.issn:2095-2651.2020.06.004
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