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Displaying similar documents to “On the subsemigroup generated by ordered idempotents of a regular semigroup”

Pointed principally ordered regular semigroups

T.S. Blyth, G.A. Pinto (2016)

Discussiones Mathematicae General Algebra and Applications

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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...

On ordered left groups.

Kehayopulu, Niovi, Tsingelis, Michael (2005)

Lobachevskii Journal of Mathematics

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On the embedding of ordered semigroups into ordered group

Mohammed Ali Faya Ibrahim (2004)

Czechoslovak Mathematical Journal

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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 L -maher and R -maher semigroups and use a technique similar to that used in [7] to show that any left reversible cancellative ordered L or R -maher semigroup can be embedded into an ordered...

On the jump number of lexicographic sums of ordered sets

Hyung Chan Jung, Jeh Gwon Lee (2003)

Czechoslovak Mathematical Journal

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Let Q be the lexicographic sum of finite ordered sets Q x over a finite ordered set P . For some P we can give a formula for the jump number of Q in terms of the jump numbers of Q x and P , that is, s ( Q ) = s ( P ) + ∑ x ∈ P s ( Q x ) , where s ( X ) denotes the jump number of an ordered set X . We first show that w ( P ) - 1 + ∑ x ∈ P s ( Q x ) ≤ s ( Q ) ≤ s ( P ) + ∑ x ∈ P s ( Q x ) , where w ( X ) denotes the width of an ordered set X . Consequently, if P is a Dilworth ordered set, that is, s ( P ) = w ( P ) - 1 , then the formula holds. We also show that it holds again if P is bipartite. Finally, we prove that the lexicographic...