Geodesic
Commutation of operations and its relationship with Menger and Mann superpositions
Discussiones Mathematicae. General Algebra and Applications, Tome 24 (2004) no. 2, pp. 153-176

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The article considers a problem from Trokhimenko paper [13] concerning the study of abstract properties of commutations of operations and their connection with the Menger and Mann superpositions. Namely, abstract characterizations of some classes of operation algebras, whose signature consists of arbitrary families of commutations of operations, Menger and Mann superpositions and their various connections are found. Some unsolved problems are given at the end of the article.
Keywords: Menger superposition, Superassociativity, (unitary) Menger algebra, selektor, n-ary groupoid, (extented) Menger multisemigroup (of operations), commutation of an operation, unar (of commutations), Mann superposition, abstract characterization of Menger algebras 
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Sokhatsky, Fedir. Commutation of operations and its relationship with Menger and Mann superpositions. Discussiones Mathematicae. General Algebra and Applications, Tome 24 (2004) no. 2, pp. 153-176. http://geodesic.mathdoc.fr/item/DMGAA_2004_24_2_a0/