The Variety of Semirings Generated by Distributive Lattices and Finite Fields
نویسندگان
چکیده
A semiring variety is d-semisimple if it is generated by the distributive lattice of order two and a finite number of finite fields. A d-semisimple variety V = HSP{B2, F1, . . . , Fk} plays the main role in this paper. It will be proved that it is finitely based, and that, up to isomorphism, the two-element distributive lattice B2 and all subfields of F1, . . . , Fk are the only subdirectly irreducible members in it.
منابع مشابه
The Semiring Variety Generated by Any Finite Number of Finite Fields and Distributive Lattices
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, B2 and all subfields of F1, . . . , Fk are the only subdirectly irreducible semirings in V.
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تاریخ انتشار 2014