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.
Keywords
Publication details
- DOI
- 10.53539/2414-536x.1404
- Journal
- Sultan Qaboos University Journal for Science, 30(2), 97-101
- Publisher
- Sultan Qaboos University
- Open access
- Gold open access
- License
- CC BY 4.0
Cite this article
APA 7
Pinto, G. (2025). N5 as a Subalgebra of a Principally Ordered Naturally Ordered Regular Semigroup with a Zero Element. Sultan Qaboos University Journal for Science, 30(2), 97-101. https://doi.org/10.53539/2414-536x.1404
MLA 9
Pinto, Gama. "N5 as a Subalgebra of a Principally Ordered Naturally Ordered Regular Semigroup with a Zero Element." Sultan Qaboos University Journal for Science, vol. 30, no. 2, 2025, pp. 97-101. https://doi.org/10.53539/2414-536x.1404.
Chicago (author–date)
Pinto, Gama. 2025. "N5 as a Subalgebra of a Principally Ordered Naturally Ordered Regular Semigroup with a Zero Element." Sultan Qaboos University Journal for Science 30 (2): 97-101. https://doi.org/10.53539/2414-536x.1404.
Harvard
Pinto, G. (2025) 'N5 as a Subalgebra of a Principally Ordered Naturally Ordered Regular Semigroup with a Zero Element', Sultan Qaboos University Journal for Science, 30(2), pp. 97-101. doi:10.53539/2414-536x.1404.
Vancouver
Pinto G. N5 as a Subalgebra of a Principally Ordered Naturally Ordered Regular Semigroup with a Zero Element. Sultan Qaboos University Journal for Science. 2025;30(2):97-101. doi:10.53539/2414-536x.1404
IEEE
G. Pinto, "N5 as a Subalgebra of a Principally Ordered Naturally Ordered Regular Semigroup with a Zero Element," Sultan Qaboos University Journal for Science, vol. 30, no. 2, pp. 97-101, 2025, doi: 10.53539/2414-536x.1404.