A Generalization of Lifting Modules

  • Amouzegar T. Kalati


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.
How to Cite
KalatiA. T. “A Generalization of Lifting Modules”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, no. 11, Nov. 2014, pp. 1477–1484, http://umj.imath.kiev.ua/index.php/umj/article/view/2239.
Research articles