JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (4): 118-126.doi: 10.6040/j.issn.1671-9352.0.2015.275

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The filters based on relative negations in FI Algebras

WU Su-peng1,2, ZHAO Bin1*   

  1. 1. College of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, Shaanxi, China;
    2. Department of Mathematics and Statistics, Ankang University, Ankang 725000, Shaanxi, China
  • Received:2015-06-08 Online:2016-04-20 Published:2016-04-08

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Abstract: The notion of relative negations in FI-algebras is proposed and some properties of it are discussed. Based on the relative negations, relative regular filters, extended relative regular filters and weak relative regular filters are defined, Some characteristic theorems of them are obtained. Algebraic properties of the set of relative double complemented elements based on the filters are introduced and the applications of extended relative regular filters are showd.

Key words: relative regular filter, weak relative regular filter, FI-algebra, extended relative regular filter

CLC Number: 

  • O141.1
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