\(E\)-rings and related structures (Q2752917)

If \(R\) is a unital ring, the left multiplications in \(R\) form a subring of the ring of additive endomorphisms of \(R\). If this subring is the full ring of additive endomorphisms, then \(R\) is called an \(E\)-ring. Similarly, an \(R\)-module \(M\) is called an \(E\)-module if the group of \(R\)-morphisms from \(R\) to \(M\) is the full group of additive homomorphisms from \(R\) to \(M\).NEWLINENEWLINENEWLINEThis paper is a survey without proofs of the major properties of \(E\)-rings and \(E\)-modules and their applications. There is also a useful list of unsolved problems in the area.NEWLINENEWLINENEWLINEIn the final section, the author presents some new results: \(R\) is a two-sided \(E\)-ring if the ring of additive endomorphisms is generated by left and right multiplications by elements of \(R\). The finite rank two-sided \(E\)-rings are classified.NEWLINENEWLINEFor the entire collection see [Zbl 0964.00012].