On some results related to Köthe's conjecture (Q2752990)

Köthe's conjecture is one of the most famous open problems in modern Ring Theory. It asks whether the existence of a nontrivial one-sided nil ideal in a ring \(R\) implies the existence of a nontrivial nil ideal in \(R\). The paper under review surveys some of the most remarkable classical and recent results related to Köthe's conjecture. A list of equivalent statements is given (note that the equivalences are very far from being obvious). Lots of open problems and results closely related to Köthe's conjecture are discussed as well. Certain classes of algebras are considered with respect to the validity of the conjecture. The bibliography is extensive, it contains 44 titles.NEWLINENEWLINENEWLINEThe survey is well written and it is a pleasure to read it. The author has contributed significantly to the ``state of art'' in this area. Let us cite only one of her recent results (mentioned in the survey). There exist simple nil algebras over any countable field.