Code properties of minimal generating sets of retracts and semiretracts (Q1345725)

Let \(A\) be a finite set and \(A^*\) be the free monoid on \(A\). A retract of \(A^*\) is a submonoid of \(A^*\) which is the image of an idempotent homomorphism from \(A^*\) to \(A^*\). A semiretract of \(A^*\) is the intersection of a family of retracts of \(A^*\). In the paper a survey is given of code properties of the minimal generating set of retracts and semiretracts. These are then used to prove properties of syntactic monoids of retracts and semiretracts.