Geodesic
The chain of right simple semigroups in ordered semigroups
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 4, Tome 227 (1995), pp. 83-88 Cet article a éte moissonné depuis la source Math-Net.Ru

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The relation $\le$ is defined on the set of right ideals of an ordered semigroup. The main result of this paper is as follows: an ordered semigroup $S$ is a chain of right simple ordered semigroups if and only if $\le$ is an order relation. Bibliography: 3 titles. 
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     author = {Niovi Kehayopulu and J. S. Ponizovskii},
     title = {The chain of right simple semigroups in ordered semigroups},
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     year = {1995},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_1995_227_a10/}
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Niovi Kehayopulu; J. S. Ponizovskii. The chain of right simple semigroups in ordered semigroups. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 4, Tome 227 (1995), pp. 83-88. http://geodesic.mathdoc.fr/item/ZNSL_1995_227_a10/