Geodesic
The Semiring Variety Generated by Any Finite Number of Finite Fields and Distributive Lattices
Publications de l'Institut Mathématique, _N_S_98 (2015) no. 112, p. 45 .

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We study the semiring variety $\mathbf{V}$ generated by any finite number of finite fields $F_1,\dots,F_k$ and two-element distributive lattice $B_2$, i.e., $\mathbf{V}=\operatorname{HSP}\{B_2,F_1,\dots,F_k\}$. It is proved that $\mathbf{V}$ is hereditarily finitely based, and that, up to isomorphism, $B_2$ and all subfields of $F_1,\dots,F_k$ are the only subdirectly irreducible semirings in $\mathbf{V}$.
DOI : 10.2298/PIM150404026S
Classification : 16Y60, 08B05 20M07
Keywords: finite field, distributive lattice, subdirectly irreducible, hereditarily finitely based, variety 
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     journal = {Publications de l'Institut Math\'ematique},
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Yong Shao; Siniša Crvenković; Melanija Mitrović. The Semiring Variety Generated by Any Finite Number of Finite Fields and Distributive Lattices. Publications de l'Institut Mathématique, _N_S_98 (2015) no. 112, p. 45 . doi : 10.2298/PIM150404026S. http://geodesic.mathdoc.fr/articles/10.2298/PIM150404026S/

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