2019
Том 71
№ 4

All Issues

Kalati Amouzegar T.

Articles: 1
Article (English)

A Generalization of Lifting Modules

Kalati Amouzegar T.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 11. - pp. 1477–1484

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.