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| 坡代数上半模的基 | |
| 引用本文： | 段俊生,惠兴杰,赵芬霞.坡代数上半模的基[J].模糊系统与数学,2010,24(3). |
| 作者姓名： | 段俊生 惠兴杰 赵芬霞 |
| 作者单位： | 1. 上海应用技术学院,理学院,上海,201418 2. 东北大学秦皇岛分校,信息与计算科学系,河北,秦皇岛,066004 3. 天津商业大学,理学院,天津,300134 |
| 基金项目： | 天津市教委科研基金资助项目 |
| 摘 要： | 有单位元的坡是加法幂等半环,在加法诱导的偏序下乘积小于等于每个因子。布尔代数、极大-极小模糊代数和任意分配格均是坡的特例。本文研究坡上半模的基。对于坡上的半模,标准基和基的基数一般都不是唯一的。我们引入既约基的概念并给出它的特征。既约基如果存在,则是唯一的。讨论了标准基和既约基之间的关系。 |
| 关 键 词： | 坡 半模 基 标准基 |
Bases of a Semimodule Over an Incline |
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| DUAN Jun-sheng,HUI Xing-jie,ZHAO Fen-xia.Bases of a Semimodule Over an Incline[J].Fuzzy Systems and Mathematics,2010,24(3). | |
| Authors: | DUAN Jun-sheng HUI Xing-jie ZHAO Fen-xia |
| Institution: | DUAN Jun-sheng1,HUI Xing-jie2,ZHAO Fen-xia3 (1. College of Science,Shanghai Institute of Technology,Shanghai 201418,China,2. Dept. of Information and Computing Science,Northeastern University at Qinhuangdao,Qinhuangdao 066004,3. College of Science,Tianjin University of Commerce,Tianjin 300134,China) |
| Abstract: | Inclines with identities are additively idempotent semirings in which products are less than or equal to either factor under the partial order induced by addition. The Boolean algebra,the max-min fuzzy algebra and any distributive lattice are all the special cases of inclines. Bases of a semimodule over an incline are studied in this paper. For a semimodule over an incline neither the standard bases nor the cardinalities of bases are unique in general. We introduce the concept of an irreducible basis and gi... |
| Keywords: | Incline Semimodule Basis Standard Basis |
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