Given a language $L$, is there a name/notation for the set $\{w^{n}\mid w\in L, n\in\mathbb N\}$?

Question

Given a language $L$, consider the operator $$\overset{*}{L}\triangleq\{w^{n}\mid w\in L, n\in\mathbb N\}.$$

This means that each word in $\overset{*}{L}$ contains of a word in $L$, concatenated to itself some number of times. Notice that this is different than $L^*$ which allows concatenation of different words in $L$.

Is there a name / known notation for this operator?

Answer 1

I would write it as follows $$ \bigcup_{w \in L} w^* $$