FREE SEMIGROUP PRESENTATIONS

Abstract

Let and  be two free semigroups. We define external direct product of two free semigroups as an ordered pair of words such  that and .We investigate the presentations of external direct product of free semigroups, state and prove under some conditions that the external direct product of two finitely generated free semigroups is finitely generated, also the external direct product of two finitely presented free semigroups is finitely presented.