THE LARGEST SOLUTION OF LINEAR EQUATION OVER THE COMPLETE HEYTING ALGEBRA  

作　　者：周惊雷 李庆国 

机构地区：[1]College of Mathematics and Econometrics, Hunan University [2]Department of Mathematics, Hunan University of Arts and Science

出　　处：《Acta Mathematica Scientia》2010年第3期810-818,共9页数学物理学报（B辑英文版）

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

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.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.

关 键 词：Complete lattice Heyting algebra linear system minimal covering 

分 类 号：O175[理学—数学]