1_ If R is a ring and a E R, let AR = {r E R I ar = OR}, Prove that AR is a subring

of R. AR is called the right annihilator of 11.

2_ Let Z* denote the ring of integers with the operations defined as: a+b = a+b-1 and a*b = a+b-a*b, The right operations are the usual addition and multiplication. Prove that Z is isomorphic to Z*

3_ Show that the first ring is not isomorphic to the second. Q and R.

Anything helps please, I know how to know when a set is a ring and more or less homomorphism, but these are really frustrating me. Thank you