"Can we find a binary operation s.t. the..." was answered by students like you

Tianna Costa

Answered question

2022-03-17

Can we find a binary operation s.t. the map

ϕ (n) = n + 1

becomes an isomorphism from

⟨ B Z, \cdot ⟩

onto

⟨ B Z, . ⟩

Meadow Franco

Beginner2022-03-18Added 6 answers

Let,

a \cdot b = (a + 1) (b + 1) - 1

.
Then,

ϕ (a \cdot b) = (a + 1) (b + 1) = ϕ (a) \cdot ϕ (b)

. I think this is correct.
Hint: Rephrase your

(B Z, +)

solution from

a + b + 1

(a + 1) + (b + 1) - 1

. Now see if you can't apply the same tactic.

Kyson Sloan

Beginner2022-03-19Added 5 answers

Hint: If

ϕ

is an isomorphism then you know the inverse. The operation is the one induced by

(Z, +)

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?