2017
Том 69
№ 9

# A Generalization of Lifting Modules

Kalati Amouzegar T.

Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 66 (2014), no. 11, pp 1654-1664.

Citation Example: Kalati Amouzegar T. A Generalization of Lifting Modules // Ukr. Mat. Zh. - 2014. - 66, № 11. - pp. 1477–1484.