| 除环的平方子环 |
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| 引用本文： | 王学宽. 除环的平方子环[J]. 湖北大学学报(自然科学版), 1998, 20(3): 205-206 |
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| 作者姓名： | 王学宽 |
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| 作者单位： | 湖北大学数学与计算机科学学院 |
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| 基金项目： | 湖北省教委自然科学基金 |
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| 摘 要： | 证明了除特征为２且为其素域上的超越扩域之无限域以外，所有除环均由其平方元素所生成；并用实例证明了特征为２且为其素域上的超越扩张之无限域中，存在不能由其平方元素所生成的域。
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| 关 键 词： | 除环 代数扩张 超越扩张 素子域 平方子环 |
The Square Subrings of Division Rings |
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| Wang Xuekuan. The Square Subrings of Division Rings[J]. Journal of Hubei University(Natural Science Edition), 1998, 20(3): 205-206 |
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| Authors: | Wang Xuekuan |
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| Abstract: | It is shown that all division rings except infinite fields of charecter 2 which are transcendental extension of their prime subfields are generated by their square elements. Pointed out that in the infinite fields of charecter 2 which are not algebra extension fields on their prime subfields, there exist fields which are not generated by their square elements. |
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| Keywords: | Division ring Algebraic extension Transcendental extension Prime subfield Infinite field |
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