Then the definition and properties of rough subrings, rough ideal and rough quotient rings are put forward and proved. Finally, homomorphism and isomorphism of rough rings is studied.
首先给出了粗糙环的定义及其性质，其次给出了粗糙子环、粗糙理想、粗糙商环的定义及其性质，最后研究了粗糙环的同态与同构。
参考来源 - 粗糙集理论在代数系统——群、环上的应用·2,447,543篇论文数据，部分数据来源于NoteExpress
建立了考虑低速干气密封端面各向同性粗糙度和静环静态角偏差的理论模型。
A theory model considering the isotropy roughness and static stator angular misalignment of dry gas seal was given.
采用化学分析、力学性能试验和金相检验等方法对该裂纹进行了分析。结果表明，此缺陷是由于试验环原始表面的粗糙度过大造成的。
By means of chemical composition analysis, mechanical property test and microstructure examination, the results showed that this defect was result of rough surface and not the crack existed in matrix.
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.
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