Geodesic
On balanced order relations and the normal hull of completely simple semirings
Discussiones Mathematicae. General Algebra and Applications, Tome 34 (2014) no. 1, pp. 75-84

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In [1] the authors proved that a semiring S is a completely simple semiring if and only if S is isomorphic to a Rees matrix semiring over a skew-ring R with sandwich matrix P and index sets I and Λ which are bands under multiplication. In this paper we characterize all the balanced order relations on completely simple semirings. Also we study the normal hull of a completely simple semiring.
Keywords: skew-ring, Rees matrix semiring, balanced order relation, essential extension, normal extension, normal ideal, normal hull 
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Maity, Sunil. On balanced order relations and the normal hull of completely simple semirings. Discussiones Mathematicae. General Algebra and Applications, Tome 34 (2014) no. 1, pp. 75-84. http://geodesic.mathdoc.fr/item/DMGAA_2014_34_1_a4/