Abstract

In this paper we will introduce the notion of $a$-connected elements of a semigroup, $a$-connected semigroups, and weakly externally commutative semigroup, and we prove that a weakly externally commutative semigroup is a semilattice of $a$-connected semigroups. Undefined notions can be found in [4].

Keywords: Semigroups; semilattice; Archimedean semigroups; externally commutative semigroup.

MSC: 20M10

Pages:  153$-$158     

Volume  61 ,  Issue  2 ,  2009