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 
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/
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[4] M. Petrich and N. Reilly, The normal hull of a completely simple semigroup, J. Algebra 81 (1983) 232-257. doi: 10.1016/0021-8693(83)90218-1.

[5] S.M. Goberstein, Balanced order relations on completely simple semigroups, Semigroup Forum 30 (1984) 121-124. doi: 10.1007/BF02573443.