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浙江大学学报（理学版）
浙江大学学报（理学版）  2017, Vol. 44 Issue (1): 33-39    DOI: 10.3785/j.issn.1008-9497.2017.01.005
数学与计算机科学     
格的反软理想
童娟1, 廖祖华1, 赵衍才1,2, 廖翠萃1, 张龙祥1, 路腾1, 吴树忠1
1. 江南大学 理学院 信息与计算科学系, 江苏 无锡 214122;
2. 无锡城市职业技术学院 基础课部, 江苏 无锡 214153
Anti-soft ideals of lattices
TONG Juan1, LIAO Zuhua1, ZHAO Yancai1,2, LIAO Cuicui1, ZHANG Longxiang1, LU Teng1, WU Shuzhong1
1. Department of Information and Computer Science, School of Science, Jiangnan University, Wuxi 214122, Jiangsu Province, China;
2. Department of Basic Science, Wuxi City College of Vocational Technology, Wuxi 214153, Jiangsu Province, China
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摘要： 首先给出了格的反软理想新概念,证明2个反软理想分别在软集的限制并和“或”运算下仍然是反软理想.其次，利用软集的反对偶给出反软理想的等价刻画.再次，利用软集的反扩张原理给出反软理想在同态映射下反像与原像的性质.最后，在全体反软理想组成的集合H上，引入链条件并讨论H是阿丁的或诺特的充要条件.
关键词： 反软理想;  软集;  反对偶;  同态;  反像    
Abstract: Firstly, the definition of anti-soft ideals is given, and we show that the restricted union and 'OR' operation of two anti-soft lattices are still anti-soft ideal. Then, we discuss the equivalent characterizations of anti-soft ideals based on the anti-dual of soft set. In addition, based on the anti-extension principle, the properties of their anti-image and inverse image are derived under the homomorphic mapping. Finally, we introduce the condition of chain over H which is composed of all the anti-soft ideals, and discuss the necessary and sufficient condition for that H is Artinian or Noetherian.
Key words: anti-soft ideal    soft set    anti-dual    homomorphism    anti-image
收稿日期: 2015-07-27 出版日期: 2017-01-22
CLC:  O159  
基金资助: 江苏省自然科学基金资助项目（BK20151117）；国家自然科学基金资助项目（61673193）
通讯作者: 廖祖华,ORCID:http://orcid:org/0000-0002-7205-664X,E-mail:liaozuhua57@163.com     E-mail: liaozuhua57@163.com
作者简介: 童娟(1992-),ORCID:http://orcid.org/0000-0002-4049-7803,女,硕士研究生,主要从事软集代数研究.
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童娟
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引用本文:

童娟, 廖祖华, 赵衍才, 廖翠萃, 张龙祥, 路腾, 吴树忠. 格的反软理想[J]. 浙江大学学报（理学版）, 2017, 44(1): 33-39.

TONG Juan, LIAO Zuhua, ZHAO Yancai, LIAO Cuicui, ZHANG Longxiang, LU Teng, WU Shuzhong. Anti-soft ideals of lattices. Journal of Zhejiang University (Science Edition), 2017, 44(1): 33-39.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2017.01.005    或    https://www.zjujournals.com/sci/CN/Y2017/V44/I1/33

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