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Ideals and free Pairs in the semigroup β ℤ

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Abstract

We prove that the equations ξ+x=mξ+y, x+ξ=y+mξ have no solutions in the semigroup β ℤ for every free ultrafilter ξ and every integer m∈0, 1. We study semigroups generated by the ultrafilters ξ, mξ. For left maximal idempotents, we prove a reduced hypothesis about elements of finite order in β ℤ.

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Authors
  1. I. V. Protasov
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Additional information

Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 4, pp. 573–580, April, 1997.

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Protasov, I.V. Ideals and free Pairs in the semigroup β ℤ. Ukr Math J 49, 635–642 (1997). https://doi.org/10.1007/BF02487327

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  • DOI: https://doi.org/10.1007/BF02487327

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