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In this paper, we study λ -constacyclic codes of length p s over the ring R = F p m [ u , v ] / ⟨ u 2 , v 2 , u v - v u ⟩ , where λ = (λ 1 + u λ 2) and (λ 1 + v λ 3) such that λ i ; i = 1 , 2 , 3 are non zero elements of F p m for prime number p. Complete ideal structure of the rings R [ x ] / ⟨ x p s - λ ⟩ has been presented. We have also discussed the dual λ -constacyclic codes over R. At last, we extend our results to λ -constacyclic codes of length 2 p s over R. [ABSTRACT FROM AUTHOR]