Results 1 to 10 of about 72 (54)
On the Semitopological Extended Bicyclic Semigroup with Adjoined Zero
Journal of Mathematical Sciences, 2022 8 pages.
Oleg Gutik
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On the closure of the extended bicyclic semigroup
Karpatsʹkì Matematičnì Publìkacìï, 2011 In the paper we study the semigroup $mathscr{C}_{mathbb{Z}}$which is a generalization of the bicyclic semigroup. We describemain algebraic properties of the semigroup$mathscr{C}_{mathbb{Z}}$ and prove that every non-trivialcongruence $mathfrak{C}$ on the
I. R. Fihel, O. V. Gutik
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The bicyclic semigroup hasP 4 *
Semigroup Forum, 1993 A semigroup \(S\) is said to have the property \(P^*_ n\), where \(n > 1\) is an integer, if for any \(s_ 1,\dots,s_ n \in S\) there exist distinct permutations \(\sigma\), \(\tau\) in the symmetric group of degree \(n\) such that \[ s_{\sigma(1)} \dots s_{\sigma(n)} = s_{\tau(1)} \dots s_{\tau(n)}. \] \textit{J. Justin} and \textit{G.
Vachuska, C ., Vachuska, P.
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Embedding the bicyclic semigroup into countably compact topological semigroups
Topology and Its Applications, 2010 We study algebraic and topological properties of topological semigroups containing a copy of the bicyclic semigroup C(p,q). We prove that each topological semigroup S with pseudocompact square contains no dense copy of C(p,q). On the other hand, we construct a (consistent) example of a pseudocompact (countably compact) Tychonov semigroup containing a ...
Taras Banakh, Oleg Gutik
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The α-bicyclic semigroup as a topological semigroup
Semigroup Forum, 1984 C. Eberhart and J. Selden showed that the only Hausdorff topology on the bicyclic semigroup which makes it a topological semigroup is the discrete topology. A related result proved in this paper is the following: Let \(W_{\alpha}\) be the \(\alpha\)-bisimple semigroup. The only locally compact Hausdorff semigroup topology on \(W_{\alpha}\) is discrete.
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Hausdorff topologies on the α-bicyclic semigroup
Semigroup Forum, 1987 The author presents a characterization of Hausdorff topologies on the \(\alpha\)-bicyclic semigroup \(W_{\alpha}\) under which \(W_{\alpha}\) is a topological inverse semigroup. Results and conditions are very technical in nature, and the author executes the steps necessary to expose these with substantial precision. The paper concludes with an example
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Identities in upper triangular tropical matrix semigroups and the bicyclic monoid [PDF]
Journal of Algebra, 2018 We establish necessary and sufficient conditions for a semigroup identity to hold in the monoid of $n\times n$ upper triangular tropical matrices, in terms of equivalence of certain tropical polynomials. This leads to an algorithm for checking whether such an identity holds, in time polynomial in the length of the identity and size of the alphabet.
Laure Daviaud +2 more
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A nonlocally compact nondiscrete topology for the α-bicyclic semigroup
Semigroup Forum, 1985 For any ordinal number \(\alpha\), let \(H_{\alpha}\) be the set of ordinal numbers less than \(\omega^{\alpha}\). The \(\alpha\)-bicyclic semigroup is \(H_{\alpha}\times H_{\alpha}\) with the operation \[ (\beta,\gamma)(\delta,\eta)=(\beta +(\max (\gamma,\delta)-\gamma,\quad \eta +(\max (\gamma,\delta)-\delta), \] where \(+\) is ordinal addition.
Annie Selden
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Математичні Студії, 2023 Let $\boldsymbol{B}_{\omega}^{\mathscr{F}}$ be the bicyclic semigroup extension for the family $\mathscr{F}$ of ${\omega}$-closed subsets of $\omega$ which is introduced in \cite{Gutik-Mykhalenych=2020}.
O. V. Gutik, M. S. Mykhalenych
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On endomorphisms of the bicyclic semigroup and the extended bicyclic semigroup
Visnyk Lvivskogo Universytetu Seriya Mekhaniko-Matematychna, 2021 It is proved that the semigroups $\mathrm{\mathbf{End}}(\boldsymbol{B}_ω)$ and $\mathrm{\mathbf{End}}(\boldsymbol{B}_{\mathbb{Z}})$ of the endomorphisms of the bicyclic semigroup $\boldsymbol{B}_ω$ and the endomorphisms of the extended bicyclic semigroup $\boldsymbol{B}_{\mathbb{Z}}$ are isomorphic to the semidirect products $(ω,+)\rtimes_φ(ω,*)$ and $\
Gutik, Oleg +2 more
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