On deformations of Gorenstein-projective modules over Nakayama and triangular matrix algebras

Let k be a fixed field of arbitrary characteristic and let ? basic connected Nakayama k-algebra without simple projective modules. In this article we prove that if V is an indecomposable finitely generated Gorenstein-projective left ?-module, then the versal deformation ring R(?,V) (in sense F. M. Bleher author) universal stable after taking syzygies. We also following result. ?=(?B0?) triangular matrix finite dimensional Gorenstein with B as ?-module ? global dimension. If (VW)f ?-module End_?((VW)f)=k, End_?(V)=k, rings R(?,(VW)f) are both isomorphic.