Quotient rings
General · Mathematics
Study notes
Q: Show ℝ[x]/(x²+1) ≅ ℂ. What is ℤ/6ℤ? In quotient: x²+1 = 0: x² = -1: x behaves as i! a+bx ↔ a+bi: map φ(a+bx) = a+bi. Kernel: multiples of x²+1 ✓. Isomorphism! ℤ/6ℤ: cosets 0..5: ≅ ℤ₆ (the integers mod 6!)! (Quotients: forcing relations!)