An embedding theorem on triangular matrix rings.

Every matrix in the triangular matrix ringover a bleached local ringRis similar to a ‘simple form’, which is, in most cases, contained in a subringofwithisomorphic to a direct product of two triangular matrix rings overRof smaller size. This result, called the embedding theorem, suggests a new approach for handling triangular matrix rings. It is applied to proving several results on the strong cleanness and strong 2-sum property of triangular matrix rings. [ABSTRACT FROM AUTHOR]