τ-倾斜τ^(-1)-倾斜模与1-Gorenstein代数

τ-tiltingτ^(-1)-tilting modules and 1-Gorenstein algebras

证明具有τ-倾斜τ^(-1)-倾斜模T的代数A的同调性质,推广1-Gorenstein代数的性质。给出例子说明代数A未必为1-Gorenstein代数。

For an algebra A admitting aτ-tiltingτ^(-1)-tilting module T,some homological properties of A are given,which generalize the homological properties of 1-Gorenstein algebras.Moreover,it is shown that A is not necessarily to be a 1-Gorenstein algebra.