I guess you proved associativity.
The law is commutative, hence you only have to find such as .
You can isolate in this equation.
I'm a little bit stuck on an assignment question.
The question is:
I already proved that (Z, *) is a semigroup. I also showed that x*e = e*x . I just don't know how to find e. (That is, if e exists at all)Let c be a fixed positive integer, and let * denote the binary operation on the set Z of integers defined be the formula
for all integers x, y, and z.
Is (Z, *) a monoid? If so, what is it's identity element?
This is what I have so far:
Any help would be much appreciated.
EDIT: I'm pretty sure it's NOT a monoid. Do you think I need to prove this though? Can I just say something along the lines of "clearly, there is no identity element" :P