Ideals and free Pairs in the semigroup β ℤ
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.
English version (Springer): Ukrainian Mathematical Journal 49 (1997), no. 4, pp 635-642.
Citation Example: Protasov I. V. Ideals and free Pairs in the semigroup β ℤ // Ukr. Mat. Zh. - 1997. - 49, № 4. - pp. 573–580.