Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (3): 810-818.doi: 10.1016/S0252-9602(10)60080-X

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THE LARGEST SOLUTION OF LINEAR EQUATION OVER THE COMPLETE HEYTING ALGEBRA

 ZHOU Jing-Lei1|2, LI Qiang-Guo1   

  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
  • Received:2007-09-02 Revised:2008-04-18 Online:2010-05-20 Published:2010-05-20
  • Supported by:

    This work was supported by the NNSF (10471035, 10771056) of China

Abstract:

Let (L, ≤, ∨, ∧) 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 ∨ and ∧ respectively, is studied. We obtain: (i) the necessary and sufficient conditions for S(A, b)≠Ø; (ii) the necessary conditions for |S(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)≠Ø.

Key words: Complete lattice, Heyting algebra, linear syste, minimal covering

CLC Number: 

  • 06D15
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