Commutation of operations and its relationship with Menger and Mann superpositions

Fedir M. Sokhatsky

Discussiones Mathematicae - General Algebra and Applications (2004)

  • Volume: 24, Issue: 2, page 153-176
  • ISSN: 1509-9415

Abstract

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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.

How to cite

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Fedir M. Sokhatsky. "Commutation of operations and its relationship with Menger and Mann superpositions." Discussiones Mathematicae - General Algebra and Applications 24.2 (2004): 153-176. <http://eudml.org/doc/287629>.

@article{FedirM2004,
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.},
author = {Fedir M. Sokhatsky},
journal = {Discussiones Mathematicae - General Algebra and Applications},
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; function algebra},
language = {eng},
number = {2},
pages = {153-176},
title = {Commutation of operations and its relationship with Menger and Mann superpositions},
url = {http://eudml.org/doc/287629},
volume = {24},
year = {2004},
}

TY - JOUR
AU - Fedir M. Sokhatsky
TI - Commutation of operations and its relationship with Menger and Mann superpositions
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2004
VL - 24
IS - 2
SP - 153
EP - 176
AB - 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.
LA - eng
KW - 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; function algebra
UR - http://eudml.org/doc/287629
ER -

References

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  12. [12] F.N. Sokhatsky, An abstract characterization (2,n)-semigroups of n-ary operations (Russian), Mat. Issled. no. 65 (1982), 132-139. 
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