Sadiki, Flamure and Ibraimi, Alit and Seferi, Ylldrita
(2018)
*Relation between associative ternary operations and neutral sequences.*
Journal of Natural Sciences and Mathematics of UT, 3 (5-6).
pp. 222-231.
ISSN 2671-3039

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## Abstract

In this paper we show relation between associative ternary operations and neutral sequences. Hence, for the operation we say that is associative ternary operation if for hold . The sequence is called i-neutral for the operation where , if . The element is called i-neutral for the operation where if the sequence is i-neutral for . In this case e is called identity for the operation . If is associative ternary operation in the set G and is 2-neutral sequence with the operation then we prove that and are i-neutral sequences with the operation , are central elements for 3-groupoid , is 1-neutral sequence if and only if is 3-neutral sequence. By the group of permutations we show that the condition of to be 2-neutral sequence, can’t replace with the other condition of being 1-neutral or 3-neutral. By the properties of associative operation implies that if for ternary operation there is at last one associative primitive binary operation then also the operation is associative.

Item Type: | Article |
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Subjects: | Q Science > Q Science (General) |

Divisions: | Faculty of Engineering, Science and Mathematics > School of Mathematics |

Depositing User: | Unnamed user with email zshi@unite.edu.mk |

Date Deposited: | 05 Jun 2019 08:35 |

Last Modified: | 05 Jun 2019 08:35 |

URI: | http://eprints.unite.edu.mk/id/eprint/166 |

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