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Æ¡Æ¡Let $R$ be a ring and $R_1$, $R_2$ its subrings such that
$R=R_1+R_2$, i.e., for every element $r\in R$ there are $r_1$ and
$r_2$ such that $r=r_1+r_2$.
Æ¡Æ¡Relations between properties of $R_1, R_2$ and those of $R$ were studied by many authors. The main studies concerned radicals and polynomial identities. The aim of the talk is to present main known results as well as several open problems. In particular the question "is $R$ nil provided that $R_1$ is nilpotent and $R_2$ is nil" is equivalent to the famous Koethe's problem. |