Gorenstein complexes over formal triangular matrix rings

Abstract

Let 𝐴 and 𝐵 be rings and 𝑈 a

-bimodule. The Gorenstein projective, injective and flat complexes over the formal triangular matrix ring

T = ( A 0 U B ) T=\bigl{(}\!\begin{smallmatrix}A&0\\ U&B\end{smallmatrix}\!\bigr{)}

are explicitly described. These statements extend some earlier results of Enochs, Cortés-Izurdiaga, Torrecillas, Zhang and Mao in this direction.