1. When is the ring of integers of a number field coverable?
- Author
-
Ayad, Mohamed and Kihel, Omar
- Subjects
Mathematics - Number Theory ,Mathematics - Commutative Algebra ,11R04, 12Y05 - Abstract
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 {\sigma}(R) 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 {\sigma}(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.
- Published
- 2023