Geodesic
All Maximal Idempotent Submonoids of Generalized Cohypersubstitutions of Type τ = (2)
Discussiones Mathematicae. General Algebra and Applications, Tome 41 (2021) no. 1, pp. 45-54

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A generalized cohypersubstitution of type τ is a mapping σ which maps every n_i-ary cooperation symbol f_i to the coterm σ(f) of type τ = (n_i)_i∈I. Denote by Cohyp_G(τ) the set of all generalized cohypersubstitutions of type τ. Define the binary operation ∘_CG on Cohyp_G(τ) by σ_1∘_CGσ_2:= σ_1^∘σ_2 for all σ_1, σ_2 ∈ Cohyp_G(τ) and σ_id(f_i) := f_i for all i ∈ I. Then Cohyp_G(τ) := {Cohyp_G(τ), ∘_CG, σ_id} is a monoid. In [5], the monoid Cohyp_G(2) was studied. They characterized and presented the idempotent and regular elements of this monoid. In this present paper, we consider the set of all idempotent elements of the monoid Cohyp_G(2) and determine all maximal idempotent submonoids of this monoid.
Keywords: generalized cohypersubstitutions, idempotent submonoids, maximal submonoids 
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Chansuriya, Nagornchat. All Maximal Idempotent Submonoids of Generalized Cohypersubstitutions of Type τ = (2). Discussiones Mathematicae. General Algebra and Applications, Tome 41 (2021) no. 1, pp. 45-54. http://geodesic.mathdoc.fr/item/DMGAA_2021_41_1_a4/