Strong Cleanness of the 2× 2 Matrix Ring over a General Local Ring
نویسنده
چکیده
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 [3] 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 determine the local rings R for which M2(R) is strongly clean.
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