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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


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Volume 63, Issue 3

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Some properties of hyperideals in ternary semihypergroups

Krisanthi Naka
  • Department of Mathematics and Computer Science, Faculty of Natural Sciences, University of Gjirokastra, Gjirokastra, Albania
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/ Kostaq Hila
  • Department of Mathematics and Computer Science, Faculty of Natural Sciences, University of Gjirokastra, Gjirokastra, Albania
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Published Online: 2013-06-28 | DOI: https://doi.org/10.2478/s12175-013-0108-3

Abstract

Ternary semihypergroups are algebraic structures with one ternary associative hyperoperation. In this paper we give some properties of left (right) and lateral hyperideals in ternary semihypergroups. We introduce the notion of left simple, lateral simple, left (0-)simple and lateral 0-simple ternary semihypergroups and characterize the minimality and maximality of left (right) and lateral hyperideals in ternary semihypergroups. The relationship between them is investigated in ternary semihypergroups extending and generalizing the analogues results for ternary semigroups.

MSC: Primary 20N20; Secondary 20N15, 20M17

Keywords: semihypergroup; ternary semihypergroup; hyperideal; left (lateral, right) hyperideal; minimal and maximal left (lateral, right) hyperideal; left (0-)simple ternary semihypergroup; lateral (0-)simple ternary semihypergroup

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About the article

Published Online: 2013-06-28

Published in Print: 2013-06-01


Citation Information: Mathematica Slovaca, Volume 63, Issue 3, Pages 449–468, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.2478/s12175-013-0108-3.

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© 2013 Mathematical Institute, Slovak Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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