ON MONOIDS OF INJECTIVE PARTIAL COFINITE SELFMAPS

We study the semigroup I-lambda(cf) of injective partial cofinite selfmaps of an infinite cardinal.. We show that I-lambda(cf) is a bisimple inverse semigroup and each chain of idempotents in I-lambda(cf) is contained in a bicyclic subsemigroup of I-lambda(cf), we describe the Green relations on I-lambda(cf) and we prove that every non-trivial congruence on I-lambda(cf) is a group congruence. Also, we describe the structure of the quotient semigroup I-lambda(cf)/sigma, where s is the least group congruence on I-lambda(cf). (C) 2015 Mathematical Institute Slovak Academy of Sciences