On monoids of injective partial cofinite selfmaps
Олег Гутік, Dusan D. Repovs · Repository of the University of Ljubljana (University of Ljubljana) · 2019
Abstract We study the semigroup I cf λ of injective partial cofinite selfmaps of an infinite cardinal λ. We show that I cf λ is a bisimple inverse semigroup and each chain of idempotents in I cf λ is contained in a bicyclic subsemigroup of I cf λ , we describe the Green relations on I cf λ and we prove that every non-trivial congruence on I cf λ is a group congruence. Also, we describe the structure of the quotient semigroup I cf λ /σ, where σ is the least group congruence on I cf λ .