A STUDY OF ARCHEMEDEAN SEMIGROUPS

Abstract

In this paper the terms, Archemedian semigroups, Strongly Archemedian semigroups are introduced. It is proved that if S is a semipseudo symmetric Archimedean semigroup then it is proved that an ideal M is maximal iff M is trivial and S has no maximal ideals if S = S2. It is also proved that in a semipseudo symmetric semigroup S containing maximal ideals if S has no semisimple elements or S is an Archimedean semigroup then and where M* is the intersection all maximal ideals of S. It is also proved that if S is a pseudo integral semigroup then it is proved that S is strongly Archimedean, S is Archimedean, S has no proper completely prime ideals, S has no proper semiprime ideals are equivalent.