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 ${mathbf V}= HSP {B_2,F_1,dots,F_{k}}$ 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.
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