加法幂等半环上线性方程的解集

Solution Sets of Linear Equations Over Additively Idempotent Semiring

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.