Ideals and free Pairs in the semigroup β ℤ

• Date: 1997
• Main Authors: Protasov, I. V., Протасов, И. В.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1997
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5033
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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....