Test Ideals in Diagonal Hypersurface Rings

Let R = k[x1,…,xn]/(xd1 + ••• + xdn), where k is a field of characteristic p, p does not divide d, and n ≥ 3. If p < d, then the test ideal for R is contained in (x1,…,xn)p − 1. If d = p + 1, then the test ideal for R is equal to (x1,…,xn)p − 1.