On a question of Mohamed and Müller

Details On a question of Mohamed and Müller On a question of Mohamed and Müller

2010-04-30

arxiv.org/abs/1004.5438v1

Mathematics

Rings and Algebras

Scientific paper

A module $M$ is called H-supplemented if for every submodule $A$ of $M$ there is a direct summand $A'$ of $M$ such that $A+X=M$ holds if and only if $A'+X=M$ for any submodule $X$ of $M$. (Equivalently, for each $X\leq M$, there exists a direct summand $D$ of $M$ such that $(X+D)/D\ll M/D$ and $(X+D)/X\ll M/X$.) Direct summands and sums of H-supplemented modules are studied and a question posed by Mohamed and M\"uller in 1990 is answered in the negative.

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