提出了半环的次极大理想的概念，讨论了半环的次极大理想的基本性质，并得到了一些相关的重要结论。
In this paper, the concept of submaximal ideal of semiring is introduced, several elementary properties of submaximal ideal are discussed, and some new conclusions are obtained.
引入了IS -代数的既约理想和次极大理想的概念，讨论了它们的性质，并得到把每个理想分解为既约理想和次极大理想的几个分解定理。
The irreducible ideal and the submaximal ideal of ISalgebras are introduced, their properties are discussed and some decomposition theorems of ideals in ISalgebras are obtained.
引入了IS -代数的既约理想和次极大理想的概念，讨论了它们的性质，并得到把每个理想分解为既约理想和次极大理想的几个分解定理。
The irreducible ideal and the submaximal ideal of ISalgebras are introduced, their properties are discussed and some decomposition theorems of ideals in ISalgebras are obtained.
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