Characteristic of a ring (2)

  1. Prove that for every commutative ring with unity, R, there is a unique ring homomorphism ϕR:ZR, and that ker(ϕR)=dR for some unique nonnegative integer dR. The number dR is called the characteristic of R and is denoted char(R).
  2. Suppose F1 and F2 are fields for which there exists a ring homomorphism f:F1F2. Prove that char(F1)=char(F2).