Rings whose additive endomorphisms are \(n\)-multiplicative. II (Q1203454)

[For part I cf. Bull. Aust. Math. Soc. 39, No. 1, 11-14 (1989; Zbl 0651.16016).] A ring \(R\) is called an \(AE_ n\)-ring, \(n\geq 2\) a positive integer, if every endomorphism \(\varphi\) of the additive group of \(R\) satisfies \(\varphi(a_ 1a_ 2\dots a_ n)=\varphi(a_ 1)\varphi(a_ 2)\dots \varphi(a_ n)\) for all \(a_ 1,\dots,a_ n\in R\). Several results concerning the structure of \(AE_ n\)-rings are obtained in this note, including an (incomplete) description of \(AE_ n\)-rings \(R\) satisfying \(R_ tR^{n-1}\neq 0\), where \(R_ t\) is the torsion ideal in \(R\).