Turning an inductor into transformer and leaving the secondary open
Don't confuse ideal transformers with real ones. Below is the model for a real transformer.



The stuff up to \$I_o\$ branch is your inductor. The rest is the transformer part. Note the first resister in that path is basically infinite when there is no load \$R_S = \infty\$ and so that whole part of the circuit can be ignored.

NOTE: Image borrowed from this cross-post.