| 半环的实理想与半实理想 |
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| 引用本文： | 肖水晶.半环的实理想与半实理想[J].南昌大学学报(理科版),2010,34(6):1. |
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| 作者姓名： | 肖水晶 |
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| 作者单位： | 南昌大学数学系； |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 在交换半环范畴中引进"半实理想","实理想"和"凸理想"等概念,从而将实代数学中有关(半)实环的主要结果推广到交换半环上。如下两个结果被建立:(1)一个半环是半实的,当且仅当它有一个实素理想;(2)半环中一个理想为实的,当且仅当它是若干个实素理想的交集。
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| 关 键 词： | 实理想 实素理想 实半环 半实半环 严格素理想 半实理想 半环 |
Real Ideals and Semireal Ideals in Commutative Semiring |
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| XIAO Shui-jing.Real Ideals and Semireal Ideals in Commutative Semiring[J].Journal of Nanchang University(Natural Science),2010,34(6):1. |
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| Authors: | XIAO Shui-jing |
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| Institution: | XIAO Shui-jing(Department of Mathematics,Nanchang University,Nanchang 330031,China) |
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| Abstract: | The notions of real ideals,semireal ideals and convex ideals are introduced in the category of commutative semirings,and some important results on real or semireal rings are generalized to commutative semirings.Two such results are established:(1) A commutative semiring is semireal,if and only if it possesses a real prime ideal;(2) An ideal of a semiring is real,if and only if it is an intersection of real prime ideals. |
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| Keywords: | semiring strictly prime ideal semireal semiring real semiring semireal ideal real ideal real prime ideal |
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