...NN AND MÁRIA B. SZENDREI 2. Preliminaries In this section we recall the notions and summarize the results of [1] needed in the paper. For the undefined notions and notation the reader is referred to =-=[2]-=- and [3]. The band of idempotents of an orthodox semigroup S is denoted by E(S), and the least inverse semigroup congruence and the least group congruence by γS and σS, respectively. If it causes no c...

...of inverse semigroups. These notions and a number of basic results are generalized in [1] for orthodox semigroups. The aim of this note is to continue these investigations. It is well known (see e.g. =-=[3]-=-) that an inverse semigroup is E-unitary and almost factorizable if and only if it is isomorphic to a semidirect product of a semilattice by a group. In this paper we give an example to show that semi...

...tion Factorizable inverse monoids and almost factorizable inverse semigroups play an important role in the theory of inverse semigroups. These notions and a number of basic results are generalized in =-=[1]-=- for orthodox semigroups. The aim of this note is to continue these investigations. It is well known (see e.g. [3]) that an inverse semigroup is E-unitary and almost factorizable if and only if it is ...