A construction of magmas and related representation

Abstract Given a magma G = ( G, · ) and a biunary algebra I = ( I, λ, ρ ) (an algebra with two unary operations), we define a new magma G I = ( G I ,· ) as follows: ( x · y )( i ) = x ( λi ) · y ( ρi ) for any x, y ∈ G I and any i ∈ I . The main goal of the paper is to characterize the variety generated by all the magmas G I obtained in this way if G and I are taken from arbitrary (but fixed) varieties of magmas and biunary algebras, respectively.