Finiteness in regular rings
The paper is mainly concerned with the solution of the following problem. Let \(R\) be a directly finite regular ring and \(M\) its maximal ideal. Is the factor ring \(R/M\) directly finite? The paper gives an example of a directly finite regular ring whose unique simple factor is not directly finite. Moreover, the ring in question has infinite stable range, which is of independent interest.
scientific article; zbMATH DE number 536660