Rings of size pq

• Ring 1

  Factor ring: Z/pq={0,1,2, ... pq-1}
  • Unity
  • Generated by a=1 with a² = a

• Ring 2

  Subset of factor ring Z/p² + Z/q² generated by a=(p,0) and b=(0,q).Matrix ring presentation: with coefficients from Z/pq, generated by:

  a= 0 0 1 0

  • No unity
  • Generated by a=1 with a² = 0 ("trivial multiplication")

• Ring 3

  Subset of factor ring Z/p + Z/q² generated by (1,0) and (0,q).
  • No unity
  • Generated by a = (1,q) with |a²| = p

• Ring 3

  Subset of factor ring Z/p² + Z/q generated by (p,0) and (0,1).
  • No unity
  • Generated by a = (p,1) with |a²| = q