Publications de l'Institut Mathématique, Nouvelle Série Vol. 98(112), pp. 45–51 (2015) 

The semiring variety generated by any finite number of finite fields and distributive latticesYong Shao, Sinisa Crvenkovic, Melanija MitrovicNorthwest University, Xian, China; Department of Mathematics and Informatics, University of Novi Sad, Serbia; Faculty of Mechanical Engineering, University of Nis, SerbiaAbstract: We study the semiring variety $\mathbf{V}$ generated by any finite number of finite fields $F_1,\dots,F_k$ and twoelement 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 $\mathbf{V}$. Keywords: finite field; distributive lattice; subdirectly irreducible; hereditarily finitely based; variety Classification (MSC2000): 16Y60; 08B05; 20M07 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 18 Nov 2015. This page was last modified: 6 Jan 2016.
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