Abbasi, M. Y.; Basar, Abul Some properties of ordered 0-minimal \((0,2)\)-bi-\(\Gamma\)-ideals in po-\(\Gamma\)-semigroups. (English) Zbl 1321.06016 Hacet. J. Math. Stat. 44, No. 2, 247-254 (2015). Summary: We introduce ordered (generalized) \((m,n)\)-\(\Gamma\)-ideals in po-\(\Gamma\)-semigroups. Then we characterize the po-\(\Gamma\)-semigroup through ordered (generalized) \((0,2)\)-\(\Gamma\)-ideals, ordered (generalized) \((1,2)\)-\(\Gamma\)-ideals and ordered (generalized) 0-minimal \((0,2)\)-\(\Gamma\)-ideals. Also, we investigate the notion of ordered (generalized) \((0,2)\)-bi-\(\Gamma\)-ideals, ordered 0-\((0,2)\) bisimple po-\(\Gamma\)-semigroups and ordered 0-minimal (generalized) \((0,2)\)-bi-\(\Gamma\)-ideals in po-\(\Gamma\)-semigroups. It is proved that a po-\(\Gamma\)-semigroup \(S\) with a zero 0 is 0-\((0,2)\)-bisimple if and only if it is left 0-simple. Cited in 2 Documents MSC: 06F99 Ordered structures 06F05 Ordered semigroups and monoids Keywords:po-\(\Gamma\)-semigroups; ordered bi-\(\Gamma\)-ideals; ordered \((m,n)\)-\(\Gamma\)-ideals; ordered \((0,2)\)-\(\Gamma\)-ideals PDFBibTeX XMLCite \textit{M. Y. Abbasi} and \textit{A. Basar}, Hacet. J. Math. Stat. 44, No. 2, 247--254 (2015; Zbl 1321.06016)