Let A be the ring
A = \{ f\in k[x] \mid f(0) = f(1) \} .Show there exists a nontrivial invertible A-module, unless k = {\mathbf F}_2. (Hint: Think about \mathop{\mathrm{Spec}}(A) as identifying 0 and 1 in {\mathbf A}^1_ k = \mathop{\mathrm{Spec}}(k[x]).)
Comments (0)