When is the ring of integers of a number field coverable?

A commutative ring R is said to be coverable if it is the union of its proper subrings and said to be finitely coverable if it is the union of a finite number of them. In the latter case, we denote by σ® the minimal number of required subrings. In this paper, we give necessary and sufficient conditions for the ring of integers A of a given number field to be finitely coverable and a formula for σ(A) is given which holds when they are met. The conditions are expressed in terms of the existence of common index divisors and (or) common divisors of values of polynomials.