Green’s Relations on the Monoid of Linear Cohypersubstitutions of Type τ = (n)

Abstract

Linear cohypersubstitutions of type τ = (n) are mappings which map the n-ary co-operation symbols to linear coterms of type τ. Every linear cohypersubstitution σ of type τ = (n) induces a mapping ŝ on the set of all linear coterms of type τ. The set of all linear cohypersubstitutions of type τ under the binary operation ocoh which is defined by σ1 ocohσ2 := 1 o σ2 for all σ1 ,σ2 ∈ Cohyplin(n) forms a monoid. In this paper, we characterize Green’s relations on Cohyplin(n).

Keywords

• linear cohypersubstitutions
• linear coterms
• superposition
• green’s relations.