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In this paper, we study the structure of cyclic, quasi-cyclic, constacycliccodes and their skew codes over the finite ring R=Z_3+vZ_3+v^2Z_3, v^3=v. TheGray images of cyclic, quasi-cyclic, skew cyclic, skew quasi-cyclic and skewconstacyclic codes over R are obtained. A necessary and sufficient conditionfor cyclic (negacyclic) codes over R that contains its dual has been given. Theparameters of quantum error correcting codes are obtained from both cyclic andnegacyclic codes over R. It is given some examples. Firstly, quasi-constacyclicand skew quasi-constacyclic codes are introduced. By giving two product, it isinvestigated their duality. A sufficient condition for 1-generator skewquasi-constacyclic codes to be free is determined.

On the codes over the Z_3+vZ_3+v^2Z_3