is multiplicative group of Q5 right?
K = Qp(5, print_mode='digits')
C1=CartesianProduct(ZZ,Integers(4));C1
Cartesian product of Integer Ring, Ring of integers modulo 4
C2=CartesianProduct(C1,Z5);C2
Cartesian product of Cartesian product of Integer Ring, Ring of integers modulo 4, 5-adic Ring with capped relative precision 20
C2.is_ring();