Publications de l'Institut Mathématique, Nouvelle SérieVol. 98(112), pp. 45–51 (2015)
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Publications de l'Institut Mathématique, Nouvelle Série Vol. 98(112), pp. 45–51 (2015) |
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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 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 $\mathbf{V}$. 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.
© 2015 Mathematical Institute of the Serbian Academy of Science and Arts
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