| 半环的正锥与序 |
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| 引用本文： | 肖水晶. 半环的正锥与序[J]. 南昌大学学报(理科版), 2011, 35(1): 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"正锥"和"序"等概念,实代数学中有关正锥和序的重要结果被推广到交换半环上。如下两个结果被建立:(1)一个半环是半实的,当且仅当它有一个正锥(或序);(2)半环中一个理想为实素理想,当且仅当它是某个序的支集。
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| 关 键 词： | 序 支集 实素理想 半环 亚正锥 半实半环 正锥 |
Positive cones and orderings in commutative semiring |
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| XIAO Shui-jing. Positive cones and orderings in commutative semiring[J]. Journal of Nanchang University(Natural Science), 2011, 35(1): 1 |
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| Authors: | XIAO Shui-jing |
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| Affiliation: | XIAO Shui-jing (Department of Mathematics,Nanchang University,Nanchang 330031,China) |
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| Abstract: | The notions of positive cones and orderings are introduced in the category of commutative semirings,and some important results on cones and orderings of commutative rings are generalized to commutative semirings.Two such results are established:(1) A commutative semiring is semireal,if and only if it possesses a positive cone(or an ordering);(2) An prime ideal of a semiring is real,if and only if it is the support of an ordering. |
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| Keywords: | semiring semireal semiring positive cone positive precone ordering real prime ideal |
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