# Abstract Algebra: Semigroups

• May 18th 2010, 02:33 PM
kiwijoey
Abstract Algebra: Semigroups
If X is a semigroup, and Tx is the set of all transformations in X, how does one show that Tx has non-commuting idempotents?
• May 18th 2010, 03:39 PM
ojones
I'm not sure you've framed your question correctly. By $T_X$ do you mean the full transformation semigroup? This is regular and idempotents commute iff it's inverse. Your statement implies that full transformation semigroups can't be inverse which is not correct.