We prove that if an ordered semigroup is a nil extension of a left strongly simple ordered semigroup, then it is left strongly archimedean, but, in contrast to the unordered case, the converse does not hold in general. However, a left strongly archimedean ordered semigroup is a nil extension of a simple ordered semigroup.
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Left quasi $$\pi $$π-regular,Intra $$\pi $$π-regular,Archimedean,Left strongly archimedean,Left strongly simple,Nil extension
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