Geodesic
On k-radicals of Green's relations in semirings with a semilattice additive reduct
Discussiones Mathematicae. General Algebra and Applications, Tome 33 (2013) no. 1, pp. 85-93

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We introduce the k-radicals of Green's relations in semirings with a semilattice additive reduct, introduce the notion of left k-regular (right k-regular) semirings and characterize these semirings by k-radicals of Green's relations. We also characterize the semirings which are distributive lattices of left k-simple subsemirings by k-radicals of Green's relations.
Keywords: k-radicals of Green's relations, left k-regular semiring, left k-simple semiring, distributive lattices of left k-simple semirings 
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     title = {On k-radicals of {Green's} relations in semirings with a semilattice additive reduct},
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Mondal, Tapas; Bhuniya, Anjan. On k-radicals of Green's relations in semirings with a semilattice additive reduct. Discussiones Mathematicae. General Algebra and Applications, Tome 33 (2013) no. 1, pp. 85-93. http://geodesic.mathdoc.fr/item/DMGAA_2013_33_1_a5/