Hey, hello. I need some help with resolving these, teacher said this would help in the test and told us to look around with these exercises. I have been revolving around with these 3, i have the other 3 resolved. These 3 really made my week frustrating. Any help with these would be appreciated please.
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
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