On Maximal Ideals of Compact Connected Topological Semigroups

Abstract

Several results concerning ideals of a compact topological semigroup 𝑆 with 𝑆2=𝑆 can be found in the literature. In this paper, we further investigate in a compact connected topological semigroup 𝑆 how the conditions 𝑆2=𝑆 and 𝑆2≠𝑆 affect the structure of ideals of 𝑆, especially the maximal ideals.