On the structure of rings which are sums of two subrings.
The paper is addressed to the following problem: Let \(R=R_1+R_2\) be a ring, where \(R_1\) is a nil ring and \(R_2\) is a reduced ring. Whether in this situation \(R_1\) is an ideal? The authors show that it is indeed in some particular cases, e.g., \(R_1\) is locally nilpotent and \(R_2\) has finite Goldie dimension, or \(R_1\) is a prime radical ring and \(R_2\) is a domain.
scientific article; zbMATH DE number 2138534