<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Two well known results on semigroups, one of them clue to Calais, the other to Lajos, are generalized in case of hypersemigroups in the way indicated in the present paper. We prove that a nonempty subset B of a regular hypersemigroup H is a bi-ideal of H if and only if it is represented in the form B = A * C where A is a right ideal and C a left ideal of H. We also show that an hyper semigroup H is regular if and only if the right and the left ideals of H are idempotent, and for every right ideal A and every left ideal B of H, the product A * B is a quasi-ideal of H. </p></abstract>

Two well known results on semigroups, one of them clue to Calais, the other to Lajos, are generalized in case of hypersemigroups in the way indicated in the present paper. We prove that a nonempty subset B of a regular hypersemigroup H is a bi-ideal of H if and only if it is represented in the form B = A * C where A is a right ideal and C a left ideal of H. We also show that an hyper semigroup H is regular if and only if the right and the left ideals of H are idempotent, and for every right ideal A and every left ideal B of H, the product A * B is a quasi-ideal of H.

On hypersemigroups

Department of Mathematics University of Athens 15784 Panepistimiopolis, Athens, Greece

Pure Mathematics and Applications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"On hypersemigroups"}

Two well known results on semigroups, one of them clue to Calais, the other to Lajos, are generalized in case of hypersemigroups in the way indicated in the...

On hypersemigroups

Published Online: Jun 24, 2016

Page range: 151 - 156

Received: Mar 07, 2016

DOI: https://doi.org/10.1515/puma-2015-0015

Keywords
hypersemigroup, regular, left (right) ideal, bi-ideal, quasi-ideal

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

On hypersemigroups

Published Online: Jun 24, 2016

Page range: 151 - 156

Received: Mar 07, 2016

DOI: https://doi.org/10.1515/puma-2015-0015

Keywordshypersemigroup, regular, left (right) ideal, bi-ideal, quasi-ideal

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
hypersemigroup, regular, left (right) ideal, bi-ideal, quasi-ideal