Abstract
We start with a basic and technical result: If S is a principally ordered regular semigroup that has a zero element, 0, then 0* is the biggest element (in fact, idempotent) of S. We obtain necessary and sufficient conditions for a principally ordered naturally ordered regular semigroup, S, with a zero element, to have as a subalgebra an ordered and algebraic isomorphic copy of N5, the smallest naturally ordered non-orthodox regular semigroup with a biggest idempotent.
Recommended Citation
Pinto, G.A.
(2025)
N5 as a Subalgebra of a Principally Ordered Naturally Ordered Regular Semigroup with a Zero Element,
Sultan Qaboos University Journal For Science: Vol. 30:
Iss.
2, 97-101.
DOI: https://doi.org/10.53539/2414-536X.1404
Available at:
https://squjs.squ.edu.om/squjs/vol30/iss2/4