On ordered regular semigroups with biggest inverses.
Pointed principally ordered regular semigroups
An ordered semigroup S is said to be principally ordered if, for every x ∈ S there exists x* = max{y ∈ 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,𝒟 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 𝒟-related. We also prove that those 𝒟-classes...
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