Let Z* denote the ring of integers with new addition and multiplication operations defined by a...

Let Z* denote the ring of integers with new addition and multiplication operations defined by a (+) b = a + b - 1 and a (*) b = a + b - ab. Prove Z (the integers) are isomorphic to Z*. Can someone please explain this to me? I get that f(1) = 0, f(2) = -1 but then f(-1) = -f(1) = 0 and f(2) = -f(2) = 1 but this does not make sense in order to define a function. Can someone explain why this is not right and show what it is correct?

Expert Solution

hheref(-1)=-f(1) represents the additive inverse of f(1) not just minus times the f(1)

in order to make isomorphism we have to map additive identity ot additive identity and multiplicative identity to multiiplicative identity

Colby Messinger answered 2 years ago

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Let Z* denote the ring of integers with new addition and multiplication operations defined by a...

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