Bi-ideals in ordered semigroups and ordered groups.
Kehayopulu, N., Ponizovskij, J.S., Tsingelis, M. (1999)
Zapiski Nauchnykh Seminarov POMI
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Displaying similar documents to “Ideals and Green's relations in ordered semigroups.”
Bi-ideals in ordered semigroups and ordered groups.
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It was shown in [7] that any right reversible, cancellative ordered semigroup can be embedded into an ordered group and as a consequence, it was shown that a commutative ordered semigroup can be embedded into an ordered group if and only if it is cancellative. In this paper we introduce the concept of -maher and -maher semigroups and use a technique similar to that used in [7] to show that any left reversible cancellative ordered or -maher semigroup can be embedded into an ordered...
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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...