Publications de l'Institut Mathematique 2015 Volume 98, Issue 112, Pages: 45-51
https://doi.org/10.2298/PIM150404026S
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The semiring variety generated by any finite number of finite fields and distributive lattices
Shao Yong (Northwest University, School of Mathematics, Xian, P.R. China)
Ren Miaomiao (Northwest University, School of Mathematics, Xian, P.R. China)
Crvenković Siniša 
(Department of Mathematics and Informatics, Novi Sad)
Mitrović Melanija (Faculty of Mechanical Engineering, Niš)
In this paper we study the semiring variety V generated by any finite number
of finite fields F1,..., Fk and two-element distributive lattice B2, i.e., V
= HSP{B2, F1,..., Fk}. It is proved that V is hereditarily finitely based,
and that, up to isomorphism, the two-element distributive lattice B2 and all
subfields of F1,..., Fk are the only subdirectly irreducible semirings in V.
Keywords: finite field, distributive lattice, subdirectly irreducible, hereditarily finitely based, variety