Abstract:

Let $T=\left(\begin{array}{ll}A & 0 \\U & B\end{array}\right)$ be a formal triangular matrix ring, where A and B are rings and U is a (B, A)-bimodule. Let $M=\left(\begin{array}{l}M_1 \\M_2\end{array}\right)_{\varphi^M}$ be a left T-module. The results are proved that if T is a left GFPI-closed and left coherent ring, U_A is flat, _BU is finitely presented and pd(_BU)<∞, then:(1) max{G-FP-id(M₁), G-FP-id(M₂)}≤G-FP-id(M); (2) G-FP-id(M)≤max{G-FP-id(M₁), G-FP-id(M₂)+1};(3) max{lG-FP-id(A), lG-FP-id(B)}≤lG-FP-id(T)≤max{lG-FP-id(A), lG-FP-id(B)+1}.

Key words: formal triangular matrix ring, Gorenstein FP-injective module, Gorenstein FP-injective dimension