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Yevhen Zelenyuk and
Yuliya Zelenyuk
Direct products of null semigroups and rectangular bands in βN
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| Published: |
March 16, 2022. |
| Keywords: |
Stone-Cech compactification, idempotent, right cancelable ultrafilter, null semigroup, rectangular band, Ramsey theory. |
| Subject: |
Primary 22A15, 05D10; Secondary 22A30, 54D80. |
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Abstract
We show that, for every m ∈ N, the direct product of the m-element null semigroup and the
2c x 2c rectangular band has copies in βN. In particular, the direct product of the 2-element null semigroup and the 2 x 2 rectangular band has copies in βN. We also point out a Ramsey theoretic consequence of the latter fact.
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| Acknowledgements
N/A
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| Author information
Yevhen Zelenyuk:
School of Mathematics
University of the Witwatersrand
Private Bag 3, Wits 2050, South Africa
yevhen.zelenyuk@wits.ac.za
Yuliya Zelenyuk:
School of Mathematics
University of the Witwatersrand
Private Bag 3, Wits 2050, South Africa
yuliya.zelenyuk@wits.ac.za
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