论文标题
清晰的元素和清除戒指
Clear elements and clear rings
论文作者
论文摘要
环$ r $中的一个元素是否是单位定型元素和单位的总和。一个关联戒指是否清楚，其每个元素是否清晰。在本文中，我们定义了清晰的环，并将许多结果扩展到更广泛的类。最后，我们证明了一个交换性的bézout域是一个基本的除数环，并且仅当其上面的每个完整矩阵订单2都是不挑剔的。
An element in a ring $R$ is called clear if it is the sum of unit-regular element and unit. An associative ring is clear if every its element is clear. In this paper we defined clear rings and extended many results to wider class. Finally, we proved that a commutative Bézout domain is an elementary divisor ring if and only if every full matrix order 2 over it is nontrivial clear.
