Geodesic
The Variety of Semirings Generated by Distributive Lattices and Finite Fields
Publications de l'Institut Mathématique, _N_S_95 (2014) no. 109, p. 101 .

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A semiring variety is \emph{d-semisimple} if it is generated by the distributive lattice of order two and a finite number of finite fields. A d-semisimple variety ${\mathbf V}={\bf HSP}\{B_2,F_1,\dots,F_{k}\}$ plays the main role in this paper. It will be proved that it is finitely based, and that, up to isomorphism, the two-element distributive lattice $B_2$ and all subfields of $F_1,\dots,F_k$ are the only subdirectly irreducible members in it.
Classification : 16Y60 08B05 20M07
Keywords: finite field, distributive lattice, subdirectly irreducible, variety 
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     title = {The {Variety} of {Semirings} {Generated} by {Distributive} {Lattices} and {Finite} {Fields}},
     journal = {Publications de l'Institut Math\'ematique},
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Yong Shao; Siniša Crvenković; Melanija Mitrović. The Variety of Semirings Generated by Distributive Lattices and Finite Fields. Publications de l'Institut Mathématique, _N_S_95 (2014) no. 109, p. 101 . http://geodesic.mathdoc.fr/item/PIM_2014_N_S_95_109_a6/