| 关于一个加法幂等元半环簇的有限基底问题 |
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| 引用本文： | 赵茜,任苗苗,张穗.关于一个加法幂等元半环簇的有限基底问题[J].纯粹数学与应用数学,2020(2):207-217. |
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| 作者姓名： | 赵茜 任苗苗 张穗 |
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| 作者单位： | 西北大学数学学院 |
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| 基金项目： | 国家自然科学基金(11701449,11971383);陕西省自然科学基础研究计划项目(2017JQ1033). |
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| 摘 要： | 研究了由x^2≈x确定的加法幂等元半环簇和xy≈zt确定的加法幂等元半环簇的并W(即包含上述两个簇的并集的最小的簇)的有限基底问题.证明了W是有限基底的,且W的子簇格是阶为312的分配格.
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| 关 键 词： | 加法幂等元半环簇 恒等式 有限基底 |
The nite basis problem for an AI-semiring variety |
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| Zhao Qian,Ren Miaomiao,Zhang Sui.The nite basis problem for an AI-semiring variety[J].Pure and Applied Mathematics,2020(2):207-217. |
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| Authors: | Zhao Qian Ren Miaomiao Zhang Sui |
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| Affiliation: | (School of Mathematics,Northwest University,Xi′an 710127,China) |
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| Abstract: | In this paper we study the finite basis problem for an AI-semiring variety W,which is the join of the AI-semiring variety defined by x^2≈x and the AI-semiring variety defined by xy≈zt.We show that W finitely based and the lattice of subvarieties of W is a distributive lattice of order 312. |
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| Keywords: | AI-semiring variety identity nitely based |
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