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On \((m,n)\)-ideals of an ordered semigroup. (English) Zbl 1307.06010

Summary: A subsemigroup \(A\) of an ordered semigroup \((S,\cdot,\leq)\) is said to be an \((m,n)\)-ideal (\(m\), \(n\) are non-negative integers) if \(A^mSA^n\subseteq A\) and \(y\leq x\) implies \(y\in A\) for any \(x\in A\), \(y\in S\). In this paper, we investigate properties of \((m,n)\)-ideals of an ordered semigroup. The results obtained are more general than the results on semigroups (without order).

MSC:

06F05 Ordered semigroups and monoids
20M12 Ideal theory for semigroups
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