Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3304
Abstract
It is shown that some embedding problems on hypersemigroups are actually problems of adjunction. According to the theorem of this paper, for every hypersemigroup $S$ which does not have identity element, an hypersemigroup $T$ having identity element can be constructed in such a way that $S$ is an ideal of $T$. Moreover, if $S$ is regular, intra-regular, right (left) regular, right (left) quasi-regular or semisimple, then so is $T$. If $A$ is an ideal, subidempotent bi-ideal or quasi-ideal of $S$, then it is an ideal, bi-ideal, quasi-ideal of $T$ as well. Illustrative examples are given.
Keywords
Hypersemigroup, identity element, ideal, adjunction, embedding, isomorphism
First Page
2834
Last Page
2853
Recommended Citation
KEHAYOPULU, NIOVI
(2022)
"Adjunction identity to hypersemigroups,"
Turkish Journal of Mathematics: Vol. 46:
No.
7, Article 18.
https://doi.org/10.55730/1300-0098.3304
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss7/18
