TY - JOUR
AU - Amouzegar T. Kalati
PY - 2014/11/25
Y2 - 2024/06/23
TI - A Generalization of Lifting Modules
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 66
IS - 11
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2239
AB - We introduce the notion of $I$ -lifting modules as a proper generalization of the notion of lifting modules and present some properties of this class of modules. It is shown that if $M$ is an $I$ -lifting direct projective module, then $S/▽$ is regular and $▽ = \text{Jac} S$, where $S$ is the ring of all $R$-endomorphisms of $M$ and $▽ = \{ϕ ∈ S | Im ϕ ≪ M\}$. Moreover, we prove that if $M$ is a projective $I$ -lifting module, then $M$ is a direct sum of cyclic modules. The connections between $I$ -lifting modules and dual Rickart modules are presented.
ER -