Auslander-Reiten conjecture for modules whose (self) dual has finite complete intersection dimension

Over a commutative Noetherian ring, we show that Auslander-Reiten conjecture holds true for the class of (finitely generated) modules whose dual has finite complete intersection dimension. Our another result validates the conjecture for the class of modules whose self dual has finite complete intersection dimension and either the module or its dual has finite Gorenstein dimension.
Comment: Theorem 3.6 in the first version is modified to Theorem 3.7 in this version. Comments and suggestions are welcome!