Publications de l'Institut Mathématique, Nouvelle Série Vol. 95[109], pp. 101–109 (2014) 

THE VARIETY OF SEMIRINGS GENERATED BY DISTRIBUTIVE LATTICES AND FINITE FIELDSYong Shao, Sinisa Crvenkovic, Melanija MitrovicNorth University, Xian, P.R. China; Department of Mathematics and Informatics, University of Novi Sad, Serbia; Faculty of Mechanical Engineering, University of Nis, SerbiaAbstract: A semiring variety is \emph{dsemisimple} if it is generated by the distributive lattice of order two and a finite number of finite fields. A dsemisimple variety ${\mathbf V}= HSP\{B_2,F_1,\dots,F_{k}\}$ plays the main role in this paper. It will be proved that it is finitely based, and that, up to isomorphism, the twoelement distributive lattice $B_2$ and all subfields of $F_1,\dots,F_k$ are the only subdirectly irreducible members in it. Keywords: finite field, distributive lattice, subdirectly irreducible, variety Classification (MSC2000): 16Y60, 08B05; 20M07 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 31 Mar 2014. This page was last modified: 2 Apr 2014.
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