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| 分配格和素域生成的半环簇 | |
| 引用本文： | 邵勇,任苗苗. 分配格和素域生成的半环簇[J]. 数学研究及应用, 2014, 34(5): 529-534 |
| 作者姓名： | 邵勇 任苗苗 |
| 作者单位： | 西北大学数学学院, 陕西 西安 710127;西北大学数学学院, 陕西 西安 710127 |
| 基金项目： | 中国博士后科学研究基金(Grant No.2011M501466);陕西省自然科学基金(Grant No.2011JQ1017). |
| 摘 要： | Let V be the variety generated by two-element distributive lattice B2 and k prime fields Fp1,...,Fpk. That is to say that V = HSP{B2, Fp1,...,Fpk}. It is proved that the variety V is finitely based. Also, the two-element distributive lattice B2 and prime fields Fp1,..., Fpk are, up to isomorphism, the only subdirectly irreducible semirings in V. Some known results are extended and enriched. |
| 关 键 词： | 分配格 半环 品种 HSP 素数域 不可约 元素 同构 |
| 收稿时间： | 2013-08-09 |
| 修稿时间： | 2014-04-16 |
The Variety of Semirings Generated by Distributive Lattices and Prime Fields |
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| Yong SHAO and Miaomiao REN. The Variety of Semirings Generated by Distributive Lattices and Prime Fields[J]. Journal of Mathematical Research with Applications, 2014, 34(5): 529-534 | |
| Authors: | Yong SHAO and Miaomiao REN |
| Affiliation: | School of Mathematics, Northwest University, Shaanxi 710127, P. R. China;School of Mathematics, Northwest University, Shaanxi 710127, P. R. China |
| 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. |
| Keywords: | prime field distributive lattice subdirectly irreducible semiring variety. |
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