| The Variety of Semirings Generated by Distributive Lattices and Prime Fields |
| Received:August 09, 2013 Revised:April 16, 2014 |
| Key Words:
prime field distributive lattice subdirectly irreducible semiring variety.
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| Fund Project:Supported by China Postdoctoral Science Foundation (Grant No.2011M501466) and the Natural Science Foundation of Shannxi Province (Grant No.2011JQ1017). |
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| Abstract: |
| Let ${\cal V}$ be the variety generated by two-element distributive lattice $B_2$ and $k$ prime fields $F_{p_{1}},\ldots,F_{p_{k}}$. That is to say that ${\cal V}={\bf HSP}\{B_{2},\,F_{p_{1}},\ldots,F_{p_{k}}\}$. It is proved that the variety ${\cal V}$ is finitely based. Also, the two-element distributive lattice $B_{2}$ and prime fields $F_{p_{1}},\ldots,F_{p_{k}}$ are, up to isomorphism, the only subdirectly irreducible semirings in ${\cal V}$. Some known results are extended and enriched. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2014.05.003 |
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