Classification of generalized ternary quadratic quasigroup functional equations of the length three

A functional equation is called: generalized if all functional variables are pairwise different; ternary if all its functional variables are ternary; quadratic if each individual variable has exactly two appearances; quasigroup if its solutions are studied only on invertible functions. A length of a...

Full description

Bibliographic Details
Main Authors:	F.M. Sokhatsky, A.V. Tarasevych
Format:	Article
Language:	English
Published:	Vasyl Stefanyk Precarpathian National University 2019-06-01
Series:	Karpatsʹkì Matematičnì Publìkacìï
Subjects:	ternary quasigroup quadratic equation length of a functional equation parastrophically primary equivalence
Online Access:	https://journals.pnu.edu.ua/index.php/cmp/article/view/1519

id	doaj-ed29a73bcdf443ae9d37398213f5e57d
record_format	Article
spelling	doaj-ed29a73bcdf443ae9d37398213f5e57d2020-11-25T02:58:42ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102019-06-0111117919210.15330/cmp.11.1.179-1921519Classification of generalized ternary quadratic quasigroup functional equations of the length threeF.M. Sokhatsky0A.V. Tarasevych1Vasyl’ Stus Donetsk National University, 21 600-richya str., 21021, Vinnytsia, UkraineKhmelnytskyi National University, 11 Instytytska str., 29016, Khmelnytskyi, UkraineA functional equation is called: generalized if all functional variables are pairwise different; ternary if all its functional variables are ternary; quadratic if each individual variable has exactly two appearances; quasigroup if its solutions are studied only on invertible functions. A length of a functional equation is the number of all its functional variables. A complete classification up to parastrophically primary equivalence of generalized quadratic quasigroup functional equations of the length three is given. Solution sets of a full family of representatives of the equivalence are found.https://journals.pnu.edu.ua/index.php/cmp/article/view/1519ternary quasigroupquadratic equationlength of a functional equationparastrophically primary equivalence
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	F.M. Sokhatsky A.V. Tarasevych
spellingShingle	F.M. Sokhatsky A.V. Tarasevych Classification of generalized ternary quadratic quasigroup functional equations of the length three Karpatsʹkì Matematičnì Publìkacìï ternary quasigroup quadratic equation length of a functional equation parastrophically primary equivalence
author_facet	F.M. Sokhatsky A.V. Tarasevych
author_sort	F.M. Sokhatsky
title	Classification of generalized ternary quadratic quasigroup functional equations of the length three
title_short	Classification of generalized ternary quadratic quasigroup functional equations of the length three
title_full	Classification of generalized ternary quadratic quasigroup functional equations of the length three
title_fullStr	Classification of generalized ternary quadratic quasigroup functional equations of the length three
title_full_unstemmed	Classification of generalized ternary quadratic quasigroup functional equations of the length three
title_sort	classification of generalized ternary quadratic quasigroup functional equations of the length three
publisher	Vasyl Stefanyk Precarpathian National University
series	Karpatsʹkì Matematičnì Publìkacìï
issn	2075-9827 2313-0210
publishDate	2019-06-01
description	A functional equation is called: generalized if all functional variables are pairwise different; ternary if all its functional variables are ternary; quadratic if each individual variable has exactly two appearances; quasigroup if its solutions are studied only on invertible functions. A length of a functional equation is the number of all its functional variables. A complete classification up to parastrophically primary equivalence of generalized quadratic quasigroup functional equations of the length three is given. Solution sets of a full family of representatives of the equivalence are found.
topic	ternary quasigroup quadratic equation length of a functional equation parastrophically primary equivalence
url	https://journals.pnu.edu.ua/index.php/cmp/article/view/1519
work_keys_str_mv	AT fmsokhatsky classificationofgeneralizedternaryquadraticquasigroupfunctionalequationsofthelengththree AT avtarasevych classificationofgeneralizedternaryquadraticquasigroupfunctionalequationsofthelengththree
_version_	1724705482402168832

Classification of generalized ternary quadratic quasigroup functional equations of the length three

Similar Items