Serial rings with right Krull dimension one
Let R be a serial ring, i.e. R is a direct sum of uniserial right ideals and R is a direct sum of uniserial left ideals. The paper starts by establishing some general properties of R and its modules. It is shown that R/Z(R) is non-singular where Z(R) is the right singular ideal of R, and every non-singular uniform R-module is uniserial. Then uniseral R- modules with Krull dimension are studied, and it is shown that R has right Krull dimension 1 if and only if R has left Krull dimension 1. These results are applied to the special case in which R is a non- singular serial ring of Krull dimension 1, and a triangular matrix representation is given for such rings.
scientific article; zbMATH DE number 4006479