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