On the variety generated by all semirings of order two

There are ten distinct two-element semirings up to isomorphism, denoted $L_2, R_2, M_2, D_2, N_2, T_2, Z_2, W_2, Z_7$, and $Z_8$ (see \cite{bk}). Among these, the multiplicative reductions of $M_2, D_2, W_2$, and $Z_8$ form semilattices, while the additive reductions of $L_2, R_2, M_2, D_2, N_2$, and $T_2$ are idempotent semilattices, commonly referred to as \emph{idempotent semirings}. In 2015, Vechtomov and Petrov \cite{vp} studied the variety generated by $M_2, D_2, W_2$, and $Z_8$, proving that it is finitely based. In the same year, Shao and Ren \cite{srii} examined the variety generated by the six idempotent semirings, demonstrating that every subvariety of this variety is finitely based. This paper systematically investigates the variety generated by all ten two-element semirings. We prove that this variety contains exactly 480 subvarieties, each of which is finitely based.