We study operads with trivial 𝔸-actions and prove an equivalence between the category of 𝔸-trivial operads and that of pseudo-graded-Perm associative algebras. As a consequence, we show that finitely generated 𝔸-trivial operads are right noetherian of integral Gelfand-Kirillov dimension and that every element in a prime 𝔸-trivial operad is central.
Li et al. (Fri,) studied this question.