Cyclic and negacyclic codes of length 4ps over $\mathbb{F}_{p^{m}}+u\mathbb{F}_{p^{m}}$

Let F(p)m be the finite field of order p(m), where p is an odd prime and m is a positive integer. In this paper, we determine the algebraic structures of all cyclic and negacyclic codes of length 4p(s) over the finite commutative chain ring R = F(p)m + uF(p)m, where u(2) = 0 and s is a positive integer. We also obtain the number of codewords in each of these codes. Among others, we establish the duals of all such codes and derive some self-dual cyclic and negacyclic codes of length 4ps over R.