Geodesic
Algebras of full terms constructed from transformations with fixed set
Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 1, pp. 127-146

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Based on the notion of full transformations with fixed set, in this paper, we present a novel concept of n-ary Fix(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 Fix(I_n,Y)-full closed identity, a Fix(I_n,Y)-full closed variety and present some concrete examples.
Keywords: transformations with fixed set, full term, Menger algebra, hypersubstitution, strongly full term, permutational full term 
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Wattanatripop, Khwancheewa; Changphas, Thawhat; Kumduang, Thodsaporn. Algebras of full terms constructed from transformations with fixed set. Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 1, pp. 127-146. http://geodesic.mathdoc.fr/item/DMGAA_2024_44_1_a8/