Baer-Kaplansky classes in categories: transfer via functors

Crivei S., Tutuncu D. , Tribak R.

COMMUNICATIONS IN ALGEBRA, 2020 (SCI İndekslerine Giren Dergi) identifier


We study the transfer of Baer-Kaplansky classes via additive functors between preadditive categories. We show that the Baer-Kaplansky property is well behaved with respect to fully faithful functors, but not with respect to their usual generalizations such as faithful, full, separable, naturally full, Maschke or dual Maschke functors. We also present the transfer of the Baer-Kaplansky property between subclasses of static and adstatic objects induced by adjoint pairs of functors. We mainly give applications to (graded) module categories and comodule categories.