a. In each case a binary operation * is given on a set M. Decide whether it is commutative or associative, whether an identity exists, and find the units.
M=N(natrual); m*n = max(m,n)
b. If M is a moniod and u in M, let sigma: M -> M be defined by sigma(a) = ua for all a in M.
(a) show that sigma is a bijection if and only if u is a unit.
(b) If u is a unit, describe the inverse mapping sigma^-1: M -> M
The Attempt at a Solution
In a, I know it is commutative and associative. I'm not sure identity and unit.
max(m,0) = always m, so 0 is identity, right?? how about unit? 0 is also unit?
in b, if u is a unit, sigma (a) = ua is gonne be identity or a???
Actually, I'm confusing about the concept of unit.