UKRAINIAN MATHEMATICAL JOURNAL, vol.75, no.10, pp.1533-1548, 2024 (SCI-Expanded)
We study the concepts of projection invariant t-extending modules and projection invariant t-Baer modules, which are generalized to the notions of pi-extending and t-Baer modules, respectively. Several structural properties are obtained and some applications are developed. It is shown that the pi-t-extending modules and pi-t-e. Baer modules are connected with each other. Moreover, we obtain a characterization for pi-t-extending modules relative to the annihilator conditions.