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On endomorphisms of the bicyclic semigroup and the extended bicyclic semigroup

Group Theory 2023-01-05 v2
Authors: Oleg Gutik , Oksana Prokhorenkova , Diana Sekh
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Abstract

It is proved that the semigroups End(Bω)\mathrm{\mathbf{End}}(\boldsymbol{B}_{\omega}) and End(BZ)\mathrm{\mathbf{End}}(\boldsymbol{B}_{\mathbb{Z}}) of the endomorphisms of the bicyclic semigroup Bω\boldsymbol{B}_{\omega} and the endomorphisms of the extended bicyclic semigroup BZ\boldsymbol{B}_{\mathbb{Z}} are isomorphic to the semidirect products (ω,+)⋊φ(ω,∗)(\omega,+)\rtimes_\varphi(\omega,*) and Z(+)⋊φ(ω,∗)\mathbb{Z}(+)\rtimes_\varphi(\omega,*), respectively.

Keywords

bicyclic semigroup extended bicyclic semigroup endomorphisms semidirect product isomorphism semigroup theory

Cite

@article{arxiv.2202.00073,
  title  = {On endomorphisms of the bicyclic semigroup and the extended bicyclic semigroup},
  author = {Oleg Gutik and Oksana Prokhorenkova and Diana Sekh},
  journal= {arXiv preprint arXiv:2202.00073},
  year   = {2023}
}

Comments

10 pages, in Ukrainian

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