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Volume :9 Issue : 2 1982      Add To Cart                                                                    Download

On universally maximal and minimal ideals

Auther : ANWAR T .AL-LAHHAM

Department of Mathematics, Faculty of Science, University of Damascus, Syria

 

ABSTRACT

 

In this paper we prove that a left ideal L of a semigroup S is the universally minimal left ideal of S if and only if LH= HL= L for all left ideals of S. A semigroup S has both the universally minimal left ideal Land the universally minimal right ideal R if and only if S has the kernel T* which is a group. In this case L * = R *= T *. A two-sided ideal A of a monoid S, with no increasing elements, is the universally maximal left, right, and two-sided ideal of S if and only if S-A is a subgroup of S. If a semigroup S with L*, R*, L*and R* has the property L* = R* = L* then either S is the union of two disjoint groups or L* is a singleton having a non-idempotent ه.

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