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
Makes and repairs jewellery such as rings, brooches, chains and bracelets, crafts objects out of precious metals, or cuts, shapes and polishes rough gemstones to produce fashion or industrial jewels.
制造和修复珠宝，使其成为戒指、胸针、手镯和工艺品。对粗糙的宝石进行切割、塑造和磨光，以使其成为时尚的工业宝石。
The rough edges of the cut branches and trunks appear like windows into the past, telling a story that the tree's rings alone cannot.
断枝断木粗糙的边缘有如通往历史的窗户，讲述了单单年轮本身所不能讲述的过往。
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