<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

Publié en ligne: 24 juin 2016

Pages: 151 - 156

Reçu: 07 mars 2016

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

Mots clés
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

Publié en ligne: 24 juin 2016

Pages: 151 - 156

Reçu: 07 mars 2016

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

Mots cléshypersemigroup, regular, left (right) ideal, bi-ideal, quasi-ideal

© 2016

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

Mots clés
hypersemigroup, regular, left (right) ideal, bi-ideal, quasi-ideal