TY - JOUR
AU - R. Alizade
AU - S. Güngör
PY - 2017/07/25
Y2 - 2024/10/03
TI - Co-coatomically supplemented modules
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 69
IS - 7
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/1742
AB - It is shown that if a submodule $N$ of $M$ is co-coatomically supplemented and $M/N$ has no maximal submodule, then $M$ is a co-coatomically supplemented module. If a module $M$ is co-coatomically supplemented, then every finitely $M$-generatedmodule is a co-coatomically supplemented module. Every left $R$-module is co-coatomically supplemented if and only if the ring $R$ is left perfect. Over a discrete valuation ring, a module $M$ is co-coatomically supplemented if and only if the basic submodule of $M$ is coatomic. Over a nonlocal Dedekind domain, if the torsion part $T(M)$ of a reduced module $M$ has a weak supplement in $M$, then $M$ is co-coatomically supplemented if and only if $M/T (M)$ is divisible and $TP (M)$ is bounded for each maximal ideal $P$. Over a nonlocal Dedekind domain, if a reduced module $M$ is co-coatomically amply supplemented, then $M/T (M)$ is divisible and $TP (M)$ is bounded for each maximal ideal $P$. Conversely, if $M/T (M)$ is divisible and $TP (M)$ is bounded for each maximal ideal $P$, then $M$ is a co-coatomically supplemented module.
ER -