Algebras of full terms constructed from transformations with fixed set

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Based on th notion of full transformations with fixed set, in this paper, we present a novel concept of n-ary F ix(I n , Y )-full terms.This term can be considered as a generalization of strongly full terms, permutational full terms and full terms.Together with the superposition operation, one can form a Menger algebra of rank n.The freeness of such algebra with respect to a variety of algebras of the same types is discussed.Furthermore, we apply hypersubstitution theory to define a F ix(I n , Y )-full closed identity, a F ix(I n , Y )-full closed variety and present some concrete examples.