On the variety generated by all semirings of order two
Abstract 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 .
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