For any prime number k ≥ 3 and any commutative ring A, we describe the subring Ak of A consisting of all sums of kth powers. For some k such as k = 11 or 19, we prove that every element of Ak is the sum of k3 kth powers (for any A). For the other k, we assume that the ring A is generated by 1 and t other elements to conclude that every element of Ak is the sum of k3t kth powers.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory