Recently, reading the book 'Skew Linear Groups' by M. Shirvani and B. A. F. Wehrfritz, I've encountered the following:
Let D be a division ring which is locally finite-dimensional over its centre but not finite dimensional over its centre.
Searching the web, I could not find the definition of being locally finite-dimensional.
The 'usual candidates' for a local property in rings are things to do with ideals, but as there are no non-trivial ideals in a division ring, the only thing that sounds remotely close is looking at finitely generated sub-algebras (when looking at $D$ as an algebra over it's centre) - is that correct? Can anyone point me to the definition of this?
Thanks in advance.