研究了半环的粗糙子半环和粗糙理想的性质；
The paper suggests the properties of rough subsemirings and rough ideal.
主要讨论对左（右）理想满足半极大条件的环与对零因子满足极大条件的环的性质。
In this pater , the proterties of the rings that satisfs the semi-maximum condition for left (right) ideal and maximum condition for zero-factor are discussed.
本文引入了半环的星元素、星理想、星同余等概念，得到了半环的星同余的一些重要性质。
In this paper, the concepts of star element, star ideals and star congruences of a semiring are introduced.
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.
给出了半环上生成模糊理想的概念并且讨论了生成模糊理想的与格相关性质，得到了令人满意的结果。
Fuzzy ideals generated by fuzzy sets and the structure of fuzzy ideals are studied, and some pretty results are obtained.
引入模糊半理想与模糊商环的概念，讨论了模糊半理想的一系列性质，并建立了关于模糊半理想的对应定理。
The concepts of fuzzy semiideal and fuzzy quotient ring is introduced and some properties of fuzzy semiideal are discussed.
本文引入了半环的星元素、星理想、星同余等概念，得到了半环的星同余的一些重要性质。
In this paper, the concepts of star element and star ideals of a semi-ring are introduced.
该文给出了一个序半环的序理想格的重要性质和一个序半环的序理想与半理想之间的关系。
This paper gives an interesting property of the lattice of order ideals of an ordered semiring and the relationship between order ideals and semiring ideals of an ordered semiring.
提出了半环的次极小理想的概念，讨论了半环的次极小理想的基本性质，并得到了一些相关的结论。
Submaximal ideal and subminimal ideal of semiring; 2. In this paper, the concept of subminimal ideal of semiring is introduced.
提出了半环的次极小理想的概念，讨论了半环的次极小理想的基本性质，并得到了一些相关的结论。
Submaximal ideal and subminimal ideal of semiring; 2. In this paper, the concept of subminimal ideal of semiring is introduced.
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