| 有理数域的子环和子环格 |
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| 引用本文： | 徐芒,喻秉钧.有理数域的子环和子环格[J].四川师范大学学报(自然科学版),2000,23(1):14-16. |
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| 作者姓名： | 徐芒 喻秉钧 |
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| 作者单位： | 四川师范大学,数学系,四川,成都,610066 |
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| 基金项目： | 国家自然科学基金(19671063)和四川省教委重点科研基金资助项目 |
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| 摘 要： | 说明了有理数域的任一子环的结构、证明了有理数域的所有子环在包含关系下所成的完备格与所有素数的集合的幂集合在包含关系下所成的完备格完备反同构。
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| 关 键 词： | 格 完备格 子环 幂集合 有理数域 |
| 文章编号： | 1001-8395（2000）01-0014-03 |
| 修稿时间： | 1999-8-19 |
The Subrings and Subring Lattice of Rational Field |
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| XU Mang,YU Bing-jun.The Subrings and Subring Lattice of Rational Field[J].Journal of Sichuan Normal University(Natural Science),2000,23(1):14-16. |
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| Authors: | XU Mang YU Bing-jun |
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| Abstract: | In this short note, the structure of any
subring of the rational field Q is described. Moreover it is proved that the complate
lattice of the set of all subrings of Q under usual inclusion is completely
anti-isomorphic with the complete lattice of the power set of the set which consists of
all prime numbers. |
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| Keywords: | Lattice Complete lattice Complete lattice anti isomorphism Subring Power set |
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