形式三角矩阵环的Gorenstein遗传性和FP-内射性

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

中文关键词:  Gorenstein (半遗传)遗传  形式三角矩阵环  FP-内射模  n-FC环

英文关键词:Gorenstein (semihereditary) hereditary  formal triangular matrix ring  $FP$-injective module  $n$-$FC$ ring

中文摘要:

      我们研究了形式三角矩阵环上模的Gorenstein(半遗传)遗传性,有限表现性和FP-内射性.给出了形式三角矩阵环是Gorenstein(半遗传)遗传的充要条件,并得出了形式三角矩阵环是n-FC环的充分条件.

英文摘要:

      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.