Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4588172 | Journal of Algebra | 2008 | 11 Pages |
Abstract
A ring R is called strongly clean if every element of R is the sum of a unit and an idempotent that commute with each other. A recent result of Borooah, Diesl and Dorsey [G. Borooah, A.J. Diesl, T.J. Dorsey, Strongly clean matrix rings over commutative local rings, J. Pure Appl. Algebra 212 (1) (2008) 281–296] completely characterized the commutative local rings R for which Mn(R) is strongly clean. For a general local ring R and n>1, however, it is unknown when the matrix ring Mn(R) is strongly clean. Here we completely characterize the local rings R for which M2(R) is strongly clean.
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