An investigation of the Baer–Kaplansky property

In this paper, we construct a local artinian ring R with Jacobson radical W such that W^2=0 , Q=R/W is commutative, dim (_QW)=1 and dim (W_Q)=2 . Then we show that, for this ring R, the category of all right R-modules Mod-R is not a Baer–Kaplansky class by proving that the class of all indecomposable right R-modules (all finitely generated right R-modules) is not Baer-Kaplansky. Finally, we give an application on some module classes over this constructed ring R.