It is known that (ℤ,⋆,⊙) where ? ⋆ ? = ? + ? − 1 and ? ⊙ ? = ? + ? − ?? is a ring. Does it have unity? Prove it.

| %).· lI. A: Y (b) (c) (d) 2. In the ring (4Z, +,.), the ideal (8) is (a) not prime (b) maximal (c) maximal and not prime (d) just ideal (b) (c) (d) 3. In the ring (Z12, +12,·12 ), the following ideal is maximal (a) (2) (b) (3) (c) (a) and (b) (d) (a) or (b)

m 2n ,ne z} their usual operations. Prove that R and R' are isomorphic rings. and R - {m+ nv2m,n ez}. 4. Assume that R are rings with respect to

Show that Q(√3, i) is the splitting field for x4 – 2x² – 3 over Q.