Journal of the
Korean Mathematical Society JKMS

The concepts of t-extending and t-Baer for modules are generalized to those of FI-t-extending and FI-t-Baer respectively. These are also generalizations of FI-extending and nonsingular quasi-Baer properties respectively and they are inherited by direct summands. We shall establish a close connection between the properties of FI-t-extending and FI-t-Baer, and give a characterization of FI-t-extending modules relative to an annihilator condition.

Keywords: nonsingular and $Z_{2}$-torsion modules, t-closed submodules, FI-extending and FI-t-extending modules, quasi-Baer and FI-t-Baer modules

MSC numbers: 16D10, 16D80, 16D70