On automorphism-invariant multiplication modules over a noncommutative ring (Q6595650)

Recall that a ring \(R\) is called \textit{right duo} if every right ideal of \(R\) is an ideal. A right \(R\)-module \(M\) is called \textit{multiplication} if for every submodule \(N\) of \(M\), there exists an ideal \(I\) of \(R\) such that \(N=MI\). So, it is easy to see that \(R\) is right duo if and only if \(R_R\) is multiplication. Also, a module \(M\) is said to be \textit{automorphism-invariant} if \(f(M)\leq M\) for any automorphism \(f\) of the injective envelope of \(M\). \textit{A. A. Tuganbaev} [J. Math. Sci., New York 123, No. 2, 3839--3905 (2004; Zbl 1097.16003)] considered the multiplication module over a non-commutative ring. In fact, this work is primarily a survey of results on multiplication modules over not necessarily commutative rings and often consider multiplication modules over right duo rings.\N\NIn this paper, the authors continue to consider the automorphism-invariance\Nof multiplication modules over a non-commutative ring.