On strongly regular rings and generalizations of semicommutative rings. (Q2909915)

Strong regularity and other properties are investigated for rings \(R\) in which left annihilators of elements are generalized weak ideals. For example, the authors prove that \(R\) is strongly regular if and only if every maximal essential right ideal \(I\) of \(R\) is YJ-injective, meaning that every nonzero element \(a\in R\) has a nonzero power \(a^n\) such that all homomorphisms from \(a^nR\) to \(I\) extend to \(R\). The same equivalence is also established in case \(R\) has the property that all right ideals of \(R\) generated by nilpotent elements are two-sided ideals. Some other equivalences, involving MELT, GP-V\('\), and SF properties, are also proved.