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 \( Z_8 \) in Bashir and Kepka (2007). 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 idempotent semirings. Vechtomov and Petrov (2015) studied the variety generated by \( M_2, D_2, W_2 \) , and \( Z_8 \) , proving that it is finitely based, while Shao and Ren (2015) 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.
