Changphas, Thawhat On \((m,n)\)-ideals of an ordered semigroup. (English) Zbl 1307.06010 Far East J. Math. Sci. (FJMS) 88, No. 2, 137-145 (2014). 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). Cited in 1 Document MSC: 06F05 Ordered semigroups and monoids 20M12 Ideal theory for semigroups Keywords:ordered semigroups; \((m,n)\)-ideals; descending chain condition for subsemigroups PDFBibTeX XMLCite \textit{T. Changphas}, Far East J. Math. Sci. (FJMS) 88, No. 2, 137--145 (2014; Zbl 1307.06010) Full Text: Link