© 2016 Elsevier B.V. The units of the chain ring [formula presented] are partitioned into a distinct types. It is shown that for any unit Λ of Type k, a unit λ of Type k ∗ can be constructed, such that the class of λ-constacyclic of length p s of Type k ∗ codes is one-to-one correspondent to the class of Λ-constacyclic codes of the same length of Type k via a ring isomorphism. The units of R a of the form Λ=Λ 0 +uΛ 1 +⋯+u a−1 Λ a−1 , where Λ 0 ,Λ 1 ,…,Λ a−1 ∈F p m , Λ 0 ≠0,Λ 1 ≠0, are considered in detail. The structure, duals, Hamming and homogeneous distances of Λ-constacyclic codes of length p s over R a are established. It is shown that self-dual Λ-constacyclic codes of length p s over R a exist if and only if a is even, and in such case, it is unique. Among other results, we discuss some conditions when a code is both α- and β-constacyclic over R a for different units α, β.