IDEMPOTENT AND REGULAR COHYPERSUBSTITUTIONS OF TYPE τ = (3)

Abstract

A mapping σ which assigns to every n-ary cooperation symbol fi an ni-ary coterm of type τ = (ni)i∈I is said to be a cohypersubstitution of type τ. The concepts of cohypersubstitutions were introduced in [Cohyperidentities and M-solid classes of coalgebras, Discrete Math.309(4) (2009) 772–783]. Every cohypersubstitution σ of type τ induces a mapping [Formula: see text] on the set of all coterms of type τ. The set of all cohypersubstitutions of type τ under the binary operation [Formula: see text] which is defined by [Formula: see text] for all σ1, σ2 ∈ Cohyp(τ) forms a monoid which is called the monoid of cohypersubstitution of type τ. In this research, we characterize all idempotent and regular elements of Cohyp(τ) where τ = (3).