- 1 47 Let X Be An Invertible Element Of A Monoid S It Is Obvious That Every Element Of The Form X With N E Z Commutes 1 (29.69 KiB) Viewed 49 times
1.47. Let x be an invertible element of a monoid S. It is obvious that every element of the form x" with n e Z commutes with x. For some elements x it may happen that these are also the only elements commuting with it. Reconsider Exercise 1.24 and show that the map f (defined by f(n) = n + 1) of the monoid Map(Z) is an example of such an element. Is the same true for g e Map(Z) defined by g(n) = n + 2?
1.24. Let f e Map(Z) be given by f(n) = n + 1 for every n e Z. Find all elements in Map(Z) that commute with f.