bicyclic semigroup
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2020 ◽  
Vol 108 (3-4) ◽  
pp. 550-556
Author(s):  
K. H. Hovsepyan


2019 ◽  
Vol 30 (02) ◽  
pp. 217-243
Author(s):  
Mohammed Abu Ayyash ◽  
Alessandra Cherubini

We give necessary and sufficient conditions in order that lower bounded HNN-extensions of inverse semigroups and HNN-extensions of finite inverse semigroups are completely semisimple semigroups. Since it is well known that an inverse semigroup is completely semisimple if and only if it does not contain a copy of the bicyclic semigroup, we first characterize such HNN-extensions containing a bicyclic subsemigroup making use of the special feature of their Schützenberger automata.



2016 ◽  
Vol 94 (1) ◽  
pp. 104-122 ◽  
Author(s):  
Berit Nilsen Givens ◽  
Amber Rosin ◽  
Karen Linton
Keyword(s):  


2014 ◽  
Vol 89 (3) ◽  
pp. 582-599
Author(s):  
G. T. Clarke ◽  
R. A. R. Monzo
Keyword(s):  


2013 ◽  
Vol 09 (08) ◽  
pp. 1961-1972 ◽  
Author(s):  
EMIL DANIEL SCHWAB

The paper deals with certain breaking processes using a compatible partition of a monoid. We introduce the broken Dirichlet convolution and the broken bicyclic semigroup. Both have a common origin and are introduced by the same elementary categorical construction.



2011 ◽  
Vol 48 (3) ◽  
pp. 342-353 ◽  
Author(s):  
Oleg Gutik ◽  
Dušan Repovš

In this paper we study the semigroup ℐ ∞↗ (ℕ) of partial cofinal monotone bijective transformations of the set of positive integers ℕ. We show that the semigroup ℐ ∞↗ (ℕ) has algebraic properties similar to the bicyclic semigroup: it is bisimple and all of its non-trivial group homomorphisms are either isomorphisms or group homomorphisms. We also prove that every locally compact topology τ on ℐ ∞↗ (ℕ) such that (ℐ ∞↗ (ℕ); τ) is a topological inverse semigroup, is discrete. Finally, we describe the closure of (ℐ ∞↗ (ℕ); τ) in a topological semigroup.



2010 ◽  
Vol 157 (18) ◽  
pp. 2803-2814 ◽  
Author(s):  
Taras Banakh ◽  
Svetlana Dimitrova ◽  
Oleg Gutik


2010 ◽  
Vol 62 (3) ◽  
pp. 607-624 ◽  
Author(s):  
F. Gourdeau ◽  
M. C. White


2008 ◽  
Vol 04 (04) ◽  
pp. 549-561 ◽  
Author(s):  
EMIL DANIEL SCHWAB ◽  
PENTTI HAUKKANEN

We show that any commutative Möbius monoid satisfies a unique factorization theorem and thus possesses arithmetical properties similar to those of the multiplicative semigroup of positive integers. Particular attention is paid to standard examples, which arise from the bicyclic semigroup and the multiplicative analogue of the bicyclic semigroup. The second example shows that the Fundamental Theorem of Arithmetic is a special case of the unique factorization theorem in commutative Möbius monoids. As an application, we study generalized arithmetical functions defined on an arbitrary commutative Möbius monoid.



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