Nuclear magnetism in n-doped semiconductors with a positive hyperfine constant is revisited. Two kinds of nuclear magnetic ordering can be induced by resident electrons in a deeply cooled nuclear spin system. At positive nuclear spin temperature below a critical value, randomly oriented nuclear spin polarons similar to that predicted by Merkulov [Phys. Solid State 40, 930 (1998)PSOSED1063-783410.1134/1.1130450] should emerge. These polarons are oriented randomly, and within each polaron, nuclear and electron spins are aligned antiferromagnetically. At negative nuclear spin temperature below a critical value, we predict another type of magnetic ordering - a dynamically induced nuclear ferromagnet. This is a long-range ferromagnetically ordered state involving both electrons and nuclei. It can form if electron spin relaxation is dominated by the hyperfine coupling, rather than by the spin-orbit interaction. Application of the theory to the n-doped GaAs suggests that ferromagnetic order may be reached at experimentally achievable nuclear spin temperature ΘN≈-0.5μK and lattice temperature TL≈5K.