| 乘法半群为逆半群的半环 |
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| 引用本文： | 邵勇,赵宪钟,潘秀娟. 乘法半群为逆半群的半环[J]. 西北大学学报(自然科学版), 2006, 36(3): 345-347 |
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| 作者姓名： | 邵勇 赵宪钟 潘秀娟 |
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| 作者单位： | 西北大学数学系 陕西西安710069 |
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| 基金项目： | 陕西省自然科学研究基金资助项目(2003A10),陕西省教育厅自然科学专项基金资助项目(02JK053) |
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| 摘 要： | 目的求证加法导出是半格、乘法导出是逆半群的半环成为分配格的充要条件。方法加法半群和乘法半群上的偏序以及二者之间的关系。结果给出了该类半环成为分配格的几个等价命题。结论推广了双半格成为分配格的一些结果。
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| 关 键 词： | 半群 半环 半格 分配格 偏序关系 |
| 文章编号： | 1000-274X(2006)03-0345-03 |
| 收稿时间： | 2004-02-09 |
| 修稿时间： | 2004-02-09 |
Semirings whose multiplicative reduct is inverse semigroup |
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| SHAO Yong,ZHAO Xian-zhong,PAN Xiu-juan. Semirings whose multiplicative reduct is inverse semigroup[J]. Journal of Northwest University(Natural Science Edition), 2006, 36(3): 345-347 |
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| Authors: | SHAO Yong ZHAO Xian-zhong PAN Xiu-juan |
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| Abstract: | Aim In order to prove a semiring whose additive reduct is a semilattice and multiplicative reduct is a inverse semigroup to be a distributive lattice.Methods Using partial orders on multiplicative reduct and additive reduct and relations between two partial orders.Results Some equivalent statements are obtained concerning a semiring becoming a distributive lattice.Conclusion Some known results about bi-semilattice becoming distributive lattice are expanded. |
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| Keywords: | semigroups semirings semilattices distributive lattices partial ordered relations |
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