“…The above notions have some strong versions, obtained by replacing direct summands by fully invariant direct summands in their definitions. E.g., see the work of Al-Saadi and Ibrahiem on (dual) strongly Rickart modules [3,4], Ebrahimi Atani, Khoramdel and Dolati Pish Hesari [21] on strongly extending modules, Wang [37] on strongly lifting modules, Crivei and Olteanu on (dual) strongly Rickart objects in abelian categories [12,13], Crivei and Radu on (dual) strongly CS-Rickart objects in abelian categories [16].…”