THE LARGEST SOLUTION OF LINEAR EQUATION OVER THE COMPLETE HEYTING ALGEBRA

作     者：周惊雷 李庆国 Zhou Jinglei 1,2 Li Qingguo 1 1.College of Mathematics and Econometrics, Hunan University, Changsha 410082, China 2.Department of Mathematics, Hunan University of Arts and Science, Changde 415000, China

作者机构：College of Mathematics and Econometrics Hunan University Department of Mathematics Hunan University of Arts and Science 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2010年第30卷第3期

页      面：810-818页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the NNSF (10471035 10771056) of China 

主　　题：Complete lattice Heyting algebra linear system minimal covering 

摘      要：Let （L, 〈, V, A） be a complete Heyting algebra. In this article, the linear system Ax = b over a complete Heyting algebra, where classical addition and multiplication operations are replaced by V and A respectively, is studied. We obtain： （i） the necessary and sufficient conditions for S（A,b）≠Ф; （ii） the necessary conditions for IS（A,b）｜ = 1. We also obtain the vector x ∈ Ln and prove that it is the largest element of S（A, b） if S（A, b）≠Ф.