GORENSTEIN HOMOLOGICAL PROPERTIES OF TENSOR RINGS.

Let $R$ be a two-sided Noetherian ring, and let $M$ be a nilpotent $R$ -bimodule, which is finitely generated on both sides. We study Gorenstein homological properties of the tensor ring $T_{R}(M)$. Under certain conditions, the ring $R$ is Gorenstein if and only if so is $T_{R}(M)$. We characterize Gorenstein projective $T_{R}(M)$ -modules in terms of $R$ -modules. [ABSTRACT FROM AUTHOR]