A Note on Idempotent Monomial Clones : Two is Strong; One is Weak (Developments of Language, Logic, Algebraic system and Computer Science)

Clones of polynomials are considered over Galois field \mathrm{G}\mathrm{F}(k) . In particular, the class of clones generated by 2‐variable idempotent polynomials is the target of our study. Our results include that the clone generated by x^{2}y^{k-2} is the largest among all such clones and the clone generated by xy^{k-1} is the smallest among all such clones. Hence, observing the exponent of one variable, two is strong and one is weak.