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高校应用数学学报
高校应用数学学报  2017, Vol. 32 Issue (3): 321-331    
    
半环的$L$-模糊理想的范畴性质
周敏
湖北民族学院 理学院, 湖北恩施 445000
The categorical properties of $L$-fuzzy ideals of semirings
ZHOU Min
Department of Mathematics, Hubei University for Nationalities, Enshi 445000, China
 全文: PDF 
摘要： 首先给出了半环的$L$-模糊理想同态的定义, 在此基础上较系统地讨论了半环的$L$-模糊理想范畴的性质, 证明了此范畴是半环范畴上的一个拓扑结构, 并探讨了其中的等子、拉回和乘积等性质. 另一方面, 给出了半环的$L$-模糊理想范畴的逆系统的定义, 建立了半环的$L$-模糊理想范畴中逆系统的逆极限结构. 特别是在引入两个逆系统之间映射的基础上, 得到了两个逆系统的逆极限之间的极限映射.
关键词： 半环;  $L$-模糊理想;  $L$-模糊理想同态;  范畴    
Abstract: The concept of $L$-fuzzy ideals of semirings is first introduced in this paper. Based on this new concept, some properties of the category of $L$-fuzzy ideal of semirings are investigated, the result that the category of $L$-fuzzy ideals of semirings is a topological construct on the category of semirings is also proved. Meanwhile, the equalizer, pullback and product are all discussed. On the other hand, the notion of inverse systems of category of $L$-fuzzy ideals of semirings is proposed and the inverse limit of the category of $L$-fuzzy ideals of semirings is constructed. Particularly, the limit mapping has been obtained by means of presenting the mapping between two inverse systems.
Key words: hemiring    $L$-fuzzy ideal    $L$-fuzzy ideal homomorphism    category
收稿日期: 2017-01-04 出版日期: 2018-04-07
:  O159  
基金资助: 国家自然科学基金(11561023; 11461025; 61473181); 湖北民族学院博士启动基金(MY2015B007); 湖北省教育厅项目(B2017090)
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引用本文:

周敏. 半环的$L$-模糊理想的范畴性质[J]. 高校应用数学学报, 2017, 32(3): 321-331.

ZHOU Min. The categorical properties of $L$-fuzzy ideals of semirings. Applied Mathematics A Journal of Chinese Universities, 2017, 32(3): 321-331.

链接本文:

http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2017/V32/I3/321

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