Topic
Cancellative semigroup
About: Cancellative semigroup is a research topic. Over the lifetime, 1320 publications have been published within this topic receiving 13319 citations.
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7 citations
TL;DR: In this paper, it was shown that each member of a class of strongly connected automata (containing all the finite ones) whose input semigroup is the semigroup of the automaton is isomorphic to an automaton (A,S,ν) where S is a semigroup for row-monomial matrices over a group G, A is a set of equivalence classes of monomial vectors over G and η is the usual product of a matrix acting on a vector.
Abstract: We show that each member of a class of strongly connected automata (containing all the finite ones) whose input semigroup is the semigroup of the automaton is isomorphic to an automaton (A,S,ν) where S is a semigroup of row-monomial matrices over a group G, A is a set of equivalence classes of monomial vectors over G and η is the usual product of a matrix acting on a vector.
7 citations
7 citations
TL;DR: In this article, the authors characterize and construct semigroups whose right regular representation is a left cancellative semigroup, called left equalizer simple semigroup, which is a special case of the semigroup with the property that the factor semigroup $S/\varrho$ is left equaliser simple.
Abstract: In this paper we characterize and construct semigroups whose right regular representation is a left cancellative semigroup. These semigroups will be called left equalizer simple semigroups. For a congruence $\varrho$ on a semigroup $S$, let ${\mathbb F}[\varrho]$ denote the ideal of the semigroup algebra ${\mathbb F}[S]$ which determines the kernel of the extended homomorphism of ${\mathbb F}[S]$ onto ${\mathbb F}[S/\varrho]$ induced by the canonical homomorphism of $S$ onto $S/\varrho$. We examine the right colons $({\mathbb F}[\varrho]:_r{\mathbb F}[S])=\{ a\in {\mathbb F}[S]:\ {\mathbb F}[S]a\subseteq {\mathbb F}[\varrho ]\}$ in general, and in that special case when $\varrho$ has the property that the factor semigroup $S/\varrho$ is left equalizer simple.
7 citations
TL;DR: In this article, the authors determine the compatible partial orders on the bicyclic semigroup B which turn it into a semilatticed semigroup, and they show that these are the only compatible orderings which turn B into a lattice ordered semigroup.
Abstract: In this paper we determine those compatible partial orders on the bicyclic semigroup B which turn it into a semilatticed semigroup. We shall see that there are exactly four distinct compatible total orderings on B. These are the only compatible orderings which turn B into a lattice ordered semigroup. On a group every compatible semilattice ordering is a lattice ordering. However this is not the case with inverse semigroups. Indeed, the situation regarding semilattice orderings on the bicyclic semigroups is much richer. There are four infinite families of compatible semilattce orderings on B. Two of these families turn B into a V-semilatticed semigroup; two of the families turn it into a ^-semilatticed semigroup.
7 citations