Gorenstein Hereditary and $FP$-Injectivity over Formal Triangular Matrix Rings

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.