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Yevhen Zelenyuk and Yuliya Zelenyuk
Three-element bands in βN view print
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| Published: |
November 26, 2015 |
| Keywords: |
Stone-Čech compactification, ultrafilter, finite band, absolute coretract. |
| Subject: |
Primary 20M10, 22A15; Secondary 22A30, 54D80. |
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Abstract
Let N be the discrete additive semigroup of natural numbers and let βN be the Stone-Čech compactification of N.
The addition on N extends to an operation + on βN making it a right topological semigroup, and to an operation ∗ making it a left topological semigroup. The semigroup (βN,∗) is the opposite of the semigroup (βN,+):
p∗ q=q+p.
We list all 3-element idempotent semigroups that have algebraic copies in (βN,+).
As a consequence we obtain that (βN,+) and (βN,∗) are not algebraically isomorphic.
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| Acknowledgements
Supported by NRF grants IFR2011033100072 and IFR1202220164.
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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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