Geodesic
On the subsemigroup generated by ordered idempotents of a regular semigroup
Discussiones Mathematicae. General Algebra and Applications, Tome 35 (2015) no. 2, pp. 205-211

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An element e of an ordered semigroup S is called an ordered idempotent if e ≤ e². Here we characterize the subsemigroup ≤(S)> generated by the set of all ordered idempotents of a regular ordered semigroup S. If S is a regular ordered semigroup then ≤(S)> is also regular. If S is a regular ordered semigroup generated by its ordered idempotents then every ideal of S is generated as a subsemigroup by ordered idempotents.
Keywords: ordered regular, ordered inverse, ordered idempotent, downward closed, completely regular 
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Bhuniya, Anjan; Kalyan Hansda, Kalyan. On the subsemigroup generated by ordered idempotents of a regular semigroup. Discussiones Mathematicae. General Algebra and Applications, Tome 35 (2015) no. 2, pp. 205-211. http://geodesic.mathdoc.fr/item/DMGAA_2015_35_2_a6/