# Is there accepted terminology for algebraic structures whose every subalgebra is free?

Is there accepted terminology for algebraic structures whose every subalgebra is free?

Examples:

• Any free group
• Any vector space
• More generally, any free module over a PID. In fact, this characterizes PID's; given a commutative unital ring $R$, every free $R$-module enjoys the property of interest iff $R$ is a PID.
• You might be interested in this mathoverflow thread. It's a different question, but related. – Alex Kruckman Oct 5 '14 at 7:34
• One might say "hereditarily free". – Zhen Lin Oct 5 '14 at 8:42