Relation between associative ternary operations and neutral sequences

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
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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