<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Based on works by Davvaz, Vougiouklis and Leoreanu-Fotea in the field of <italic>n</italic>–ary hyperstructures and binary relations we present a construction of <italic>n</italic>–ary hyperstructures from binary quasi-ordered semigroups. We not only construct the hyperstructures but also study their important elements such as identities, scalar identities or zeros. We also relate the results to earlier results obtained for a similar binary construction and include an application of the results on a hyperstructure of linear differential operators.</p></abstract>

Based on works by Davvaz, Vougiouklis and Leoreanu-Fotea in the field of n–ary hyperstructures and binary relations we present a construction of n–ary hyperstructures from binary quasi-ordered semigroups. We not only construct the hyperstructures but also study their important elements such as identities, scalar identities or zeros. We also relate the results to earlier results obtained for a similar binary construction and include an application of the results on a hyperstructure of linear differential operators.

<italic>n</italic>–ary hyperstructures constructed from binary quasi–ordered semigroups

Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 8, 616 00 Brno, Czech Republic.

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

–ary hyperstructures constructed from binary quasi–ordered semigroups

Based on works by Davvaz, Vougiouklis and Leoreanu-Fotea in the field of n–ary hyperstructures and binary relations we present a construction of n–ary...

n–ary hyperstructures constructed from binary quasi–ordered semigroups

Published Online: Dec 22, 2015

Page range: 147 - 168

Received: Jul 25, 2013

Accepted: Oct 08, 2013

DOI: https://doi.org/10.2478/auom-2014-0056

Keywords
hyperstructures, –ary hyperstructures, partially ordered and quasi-ordered sets

© 2014 Michal Novák, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

n–ary hyperstructures constructed from binary quasi–ordered semigroups

Published Online: Dec 22, 2015

Page range: 147 - 168

Received: Jul 25, 2013

Accepted: Oct 08, 2013

DOI: https://doi.org/10.2478/auom-2014-0056

Keywordshyperstructures, –ary hyperstructures, partially ordered and quasi-ordered sets

© 2014 Michal Novák, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
hyperstructures, –ary hyperstructures, partially ordered and quasi-ordered sets