Strongly Clean Matrix Rings over Commutative Rings

Abstract

A ring R is called strongly clean if every element of R is the sum of a unit and an idempotent that commute. By SRC factorization, Borooah, Diesl, and Dorsey [3] completely determined when Mn(R) over a commutative local ring R is strongly clean. We generalize the notion of SRC factorization to commutative rings, prove that commutative n-SRC rings (n ≥ 2) are precisely the commutative local rings over which Mn(R) is strongly clean, and characterize strong cleanness of matrices over commutative projective-free rings having ULP. The strongly π-regular property (hence, strongly clean property) of Mn(C(X,C)) with X a P-space relative to C is also obtained where C(X,C) is the ring of complex valued continuous functions.

Cite this paper

@inproceedings{Fan2008StronglyCM, title={Strongly Clean Matrix Rings over Commutative Rings}, author={Lingling Fan and Xiande Yang}, year={2008} }