Geodesic
Pointed principally ordered regular semigroups
Discussiones Mathematicae. General Algebra and Applications, Tome 36 (2016) no. 1, pp. 101-111 Cet article a éte moissonné depuis la source Library of Science

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An ordered semigroup S is said to be principally ordered if, for every x ∈ S there exists x* = maxy ∈ S | xyx ⩽ x. Here we investigate those principally ordered regular semigroups that are pointed in the sense that the classes modulo Green's relations ℒ,ℛ, have biggest elements which are idempotent. Such a semigroup is necessarily a semiband. In particular we describe the subalgebra of (S;*) generated by a pair of comparable idempotents that are -related. We also prove that those -classes which are subsemigroups are ordered rectangular bands.
Keywords: regular semigroup, principally ordered, naturally ordered, Green's relations 
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Blyth, T.; Pinto, G. Pointed principally ordered regular semigroups. Discussiones Mathematicae. General Algebra and Applications, Tome 36 (2016) no. 1, pp. 101-111. http://geodesic.mathdoc.fr/item/DMGAA_2016_36_1_a7/

[1] T.S. Blyth, Lattices and Ordered Algebraic Structures (Springer, 2005). doi: 10.1007/b139095

[2] T.S. Blyth and M.F. Janowitz, Residuation Theory (Pergamon, 1972).

[3] T.S. Blyth and G.A. Pinto, Principally ordered regular semigroups, Glasgow Math. J. 32 (1990), 349-364. doi: 10.1017/S0017089500009435

[4] T.S. Blyth and G.A. Pinto, Idempotents in principally ordered regular semigroups, Communications in Algebra 19 (1991), 1549-1563. doi: 10.1080/00927879108824220

[5] T.S. Blyth and M.H. Almeida Santos, On weakly multiplicative inverse transversals, Proc. Edinburgh Math. Soc. 37 (1993), 93-99. doi: 10.1017/S001309150001871X

[6] P.M. Higgins, Techniques of Semigroup Theory (Oxford Science Publiications, 1992). doi: 10.1007/BF02573500