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2015•Publications de l Institut MathematiqueOpen access

The semiring variety generated by any finite number of finite fields and distributive lattices

Yong Shao, Miaomiao Ren, Siniša Crvenković, Melanija Mitrović

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Abstract

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.

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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.

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Available abstract

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.

Key concepts: Distributive property, Distributive lattice, Mathematics, Semiring, Isomorphism (crystallography), Variety (cybernetics), Lattice (music), Pure mathematics

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