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On the embedding of ordered semigroups into ordered group

Mohammed Ali Faya Ibrahim (2004)

Czechoslovak Mathematical Journal

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 group.

On the Frobenius number of a modular Diophantine inequality

José Carlos Rosales, P. Vasco (2008)

Mathematica Bohemica

We present an algorithm for computing the greatest integer that is not a solution of the modular Diophantine inequality a x mod b ≤ x , with complexity similar to the complexity of the Euclid algorithm for computing the greatest common divisor of two integers.

On the graph labellings arising from phylogenetics

Weronika Buczyńska, Jarosław Buczyński, Kaie Kubjas, Mateusz Michałek (2013)

Open Mathematics

We study semigroups of labellings associated to a graph. These generalise the Jukes-Cantor model and phylogenetic toric varieties defined in [Buczynska W., Phylogenetic toric varieties on graphs, J. Algebraic Combin., 2012, 35(3), 421–460]. Our main theorem bounds the degree of the generators of the semigroup by g + 1 when the graph has first Betti number g. Also, we provide a series of examples where the bound is sharp.

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