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Discussiones Mathematicae General Algebra and Applications 24(2) (2004) 153-176
DOI: https://doi.org/10.7151/dmgaa.1082

COMMUTATION OF OPERATIONS AND ITS RELATIONSHIP WITH MENGER AND MANN SUPERPOSITIONS

Fedir M. Sokhatsky

Tymirazieva str., 27, apt. 6
Vinnytsia 21001, Ukraine
e-mail: fedir@vinnitsa.com

Abstract

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.

2000 Mathematics Subject Classification: 08A40, 08A55, 20N05, 20N15, 20M20, 20M30.

References

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Received 14 July 2001
Revised 27 December 2001
Revised 3 August 2004
Revised 27 November 2004