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A Note on Clean Rings.
- Source :
-
Algebra Colloquium . Sep2007, Vol. 14 Issue 3, p537-540. 4p. - Publication Year :
- 2007
-
Abstract
- Let R be a ring and g(x) a polynomial in C[x], where C=C(R) denotes the center of R. Camillo and Simón 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 ∈ C, the ring R is clean and b-a is invertible in R if and only if R is g1(x)-clean, where g1(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–Simón Theorem is indeed equivalent to the notion of clean rings. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10053867
- Volume :
- 14
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Algebra Colloquium
- Publication Type :
- Academic Journal
- Accession number :
- 25602556
- Full Text :
- https://doi.org/10.1142/S1005386707000491