E-special Ordered Regular Semigroups |
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Authors: | T S Blyth M H Almeida Santos |
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Institution: | 1. Mathematical Institute , University of St. Andrews , St. Andrews , Scotland tsblyth.prof@btinternet.com tsb@st-and.ac.uk;3. Centro de Matemática e Aplica??es (CMA) , FCT , UNLDepartamento de Matemática, FCT, UNL, Monte da Caparica, Portugal |
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Abstract: | An ordered regular semigroup S is E-special if for every x ∈ S there is a biggest x + ∈ S such that both xx + and x + x are idempotent. Every regular strong Dubreil–Jacotin semigroup is E-special, as is every ordered completely simple semigroup with biggest inverses. In an E-special ordered regular semigroup S in which the unary operation x → x + is antitone the subset P of perfect elements is a regular ideal, the biggest inverses in which form an inverse transversal of P if and only if S has a biggest idempotent. If S + is a subsemigroup and S does not have a biggest idempotent, then P contains a copy of the crown bootlace semigroup. |
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Keywords: | Crown bootlace semigroup Dubreil–Jacotin semigroup E-special Inverse transversal |
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