加法幂等半环上线性方程的解集  

Solution Sets of Linear Equations Over Additively Idempotent Semiring

作　　者：章怀方 舒乾宇 ZHANG Huai-fang;SHU Qian-yu(College of Mathematics Science Sichuan Normal University,Chengdu 610066 P.R.China)

机构地区：[1]四川师范大学数学科学学院,成都四川610066

出　　处：《模糊系统与数学》2024年第1期44-53,共10页Fuzzy Systems and Mathematics

摘　　要：本文在有最大元的交换加法幂等半环中讨论了线性方程组的解集问题.首先,在6是可加既约元的条件下,我们找到了这类加法幂等半环上的线性方程有解的充要条件,并且表示出了线性方程的解集;其次,在bi是可加既约元的条件下,通过加法幂等半环上的线性不等式组的解集,得到了线性方程组的解集.In this paper,we discuss some problems about linear equations over commutative additively idempotent semirings.First,when b is additive irreducible element,we give some necessary and sufficient conditions for the linear equation is solvable over additively idempotent semiring and describe the solution set of the linear equation.Secondly,when b,is additive irreducible element,we obtain the solution set of linear equations by the solution set of linear ine-quality equations.

关 键 词：加法幂等半环 极小解 最大解 解集 

分 类 号：O159[理学—数学]