Results 31 to 40 of about 137 (87)

Avoidable Sets in The Bicyclic Inverse Semigroup

Ars Comb., 2005
A subset $U$ of a set $S$ with a binary operation is called {\it avoidable} if $S$ can be partitioned into two subsets $A$ and $B$ such that no element of $U$ can be written as a product of two distinct elements of $A$ or as the product of two distinct elements of $B$. The avoidable sets of the bicyclic inverse semigroup are classified.
openaire   +2 more sources

Units of Integral Semigroup Rings

, 1996
It is proved that both the Bass cyclic and bicyclic units generate a subgroup of finite index in U(ZS), assumingSis a finite semigroup such thatQSis semisimple Artinian and does not contain certain types of simple ...
Wang, Duzhong, Jespers, Eric
core   +1 more source

Polyhedral convex cones and the equational theory of the bicyclic semigroup [PDF]

Journal of the Australian Mathematical Society, 2006
AbstractTo any given balanced semigroup identityU≈Wa number of polyhedral convex cones are associated. In this setting an algorithm is proposed which determines whether the given identity is satisfied in the bicylic semigroupor in the semigroup. The semigroupsBCandEdeserve our attention because a semigroup variety contains a simple semigroup which is ...
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On topologization of the extended bicyclic semigroup

Bukovinian Mathematical Journal
On the extended bicyclic semigroup $\mathscr{C}_\mathbb{Z}$ the following non-discrete $T_1$-topologies are constructed: $(i)$ a semigroup inverse topology; $(ii)$ a Baire left-continuous [right-continuous] topology; $(iii)$ a locally compact left-continuous [right-continuous] topology.
Oleg Gutik, Marharyta Zolotar, Oleksandra Lysetska   +2 more
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On the lattice of weak topologies on the bicyclic monoid with adjoined zero

, 2020
A Hausdorff topology τ on the bicyclic monoid with adjoined zero C⁰ is called weak if it is contained in the coarsest inverse semigroup topology on C⁰. We show that the lattice W of all weak shift-continuous topologies on C⁰ is isomorphic to the lattice
Gutik, O., Bardyla, S.
core   +1 more source

On the semigroup of injective endomorphisms of the semigroup $\boldsymbol{B}_{\omega}^{\mathscr{F}_n}$ which is generated by the family $\mathscr{F}_n$ of initial finite intervals of $\omega$

, 2022
In the paper we describe injective endomorphisms of the inverse semigroup $\boldsymbol{B}_{\omega}^{\mathscr{F}}$, which is introduced in the paper [O. Gutik and M. Mykhalenych, \emph{On some generalization of the bicyclic monoid}, Visnyk Lviv. Univ. Ser.
Popadiuk, Olha, Gutik, Oleg
core  

Bicyclic semigroups of left I-quotients

, 2011
In this article we study left I-orders in the bicyclic monoid $\mathcal{B}$. We give necessary and sufficient conditions for a subsemigroup of $\mathcal{B}$ to be a left I-oreder in $\mathcal{B}$. We then prove that any left I-order in $\mathcal{B}$ is straight.
openaire   +3 more sources

Semigroup presentations

, 2012
In this thesis we consider in detail the following two fundamental problems for semigroup presentations: 1. Given a semigroup find a presentation defining it. 2. Given a presentation describe the semigroup defined by it.
Ruškuc, Nik
core  

Cayley automaton semigroups

, 2015
Let S be a semigroup, C(S) the automaton constructed from the right Cayley graph of S with respect to all of S as the generating set and ∑(C(S)) the automaton semigroup constructed from C(S). Such semigroups are termed Cayley automaton semigroups. For
McLeman, Alexander Lewis Andrew
core  

Умови, за яких напівгрупа Брандта неізоморфна варіанту.

, 2019
In this paper we study the question if the Brandt semigroup can be a variant of another semigroup or not. For a semigroup which does not contain a bicyclic subsemigroup we proved that a variant of such semigroup is not a Brandt semigroup. For an infinite
Desiateryk, O.O.
core   +1 more source