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Abstract
An ordered regular semigroup, , is said to be principally ordered if for every there exists . A principally ordered regular semigroup is pointed if for every element, we have . Here we investigate those principally ordered regular semigroups that are eventually pointed in the sense that for all there exists a positive integer, , such that . Necessary and sufficient conditions for an eventually pointed principally ordered regular semigroup to be naturally ordered and to be completely simple are obtained. We describe the subalgebra of generated by a pair of comparable idempotents and such that .
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References
- Blyth, T.S. and Pinto, G.A. Principally ordered regular semigroups, Glasgow Mathematics Journal. 32 (1990) 349-364. doi:10.1017/S0017089500009435.
- Blyth, T.S. and Pinto, G.A. Idempotents in principally ordered regular semigroups, Communications in Algebra 19 (1991) 1549-1563. doi:10.1080/00927879108824220.
- Blyth, T.S. Lattices and Ordered Algebraic Structures, (Springer 2005). doi:10.1007/b139095.
- Blyth, T.S. and Pinto, G.A. Pointed principally ordered regular semigroups, Discussiones Mathematicae 36 (2016) 101-111. doi:10.7151/dmgaa.1243.
- Higgins, P.M. Techniques of Semigroup Theory (Oxford Science Publications, 1992) doi:10.1007/BF02573500.
References
Blyth, T.S. and Pinto, G.A. Principally ordered regular semigroups, Glasgow Mathematics Journal. 32 (1990) 349-364. doi:10.1017/S0017089500009435.
Blyth, T.S. and Pinto, G.A. Idempotents in principally ordered regular semigroups, Communications in Algebra 19 (1991) 1549-1563. doi:10.1080/00927879108824220.
Blyth, T.S. Lattices and Ordered Algebraic Structures, (Springer 2005). doi:10.1007/b139095.
Blyth, T.S. and Pinto, G.A. Pointed principally ordered regular semigroups, Discussiones Mathematicae 36 (2016) 101-111. doi:10.7151/dmgaa.1243.
Higgins, P.M. Techniques of Semigroup Theory (Oxford Science Publications, 1992) doi:10.1007/BF02573500.