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Some properties of ordered 0-minimal \((0,2)\)-bi-\(\Gamma\)-ideals in po-\(\Gamma\)-semigroups. (English) Zbl 1321.06016

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.

MSC:

06F99 Ordered structures
06F05 Ordered semigroups and monoids
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