On Ordered Semigroups Containing Covered Ideals

Abstract

A proper ideal M of an ordered semigroup (S, ·, ≤) is said to be a covered ideal of S if M ⊆ (S(S∖M)S], i.e., if for any x in M, there exist a, c in S and b in S∖M such that x ≤ abc. The purpose of this article is to study the structure of ordered semigroups containing covered ideals. The results obtained generalize the results on semigroups (without order) studied by Fabrici in 1984.

Key Words:

• Covered ideal
• Left (right two-sided) ideal
• Maximal ideal
• Ordered semigroup
• Semigroup
• Two-sided base

2010 Mathematics Subject Classification:

• 06F05