Commuting map on semigroup of binary operations

Abstract

This paper explores the algebraic structure of the magma monoid (M(S), /), where M(S) comprises all binary operations on S. We investigate the notion of the center of the monoid and introduce a commuting map τ_∗ for each element ∗∈M(S). Furthermore, we characterize the commuting maps for all commutative elements in M(S).