A note on clean rings

作者：Wang Zhou^*; Chen Jianlong

来源：Algebra Colloquium, 2007, 14(3): 537-540.

• clean rings
• g(x)-clean rings
• group rings

Let R be a ring and g(x) a polynomial in C[x], where C = C(R) denotes the center of R. Camillo and Simon called the ring g(x)-clean if every element of R can be written as the sum of a unit and a root of g(x). In this paper, we prove that for a, b is an element of C, the ring R is clean and b - a is invertible in R if and only if R is g(1)(x)-clean, where g(1)(x) = (x - a) (x - b). This implies that in some sense the notion of g(x)-clean rings in the Nicholson-Zhou Theorem and in the Camillo-Simon Theorem is indeed equivalent to the notion of clean rings.

• 出版日期2007-9
• 单位东南大学