CENTRALIZERS IN THE SEMIGROUP OF INJECTIVE TRANSFORMATIONS ON AN INFINITE SET
Janusz Konieczny · Bulletin of the Australian Mathematical Society · 2010
Abstract For an infinite setX, denote by Γ(X) the semigroup of all injective mappings fromXtoX. Forα∈Γ(X), letC(α)={β∈Γ(X):αβ=βα} be the centralizer ofαin Γ(X). For an arbitraryα∈Γ(X), we characterize the elements ofC(α) and determine Green’s relations inC(α), including the partial orders of ℒ-, ℛ-, and 𝒥-classes.