Not all Anarchists are the same, but most are Anarcho-Communists and reject states, classes, money, wage labour, (commercial) property, and believe in everyone being taken care of. In this way Anarchism and (real) Communism are the absence of a system, even a sort of anti-system, because they see imposed systems as the problem.

However, you are right that 'ownership' even 'common ownership' is open to misinterpretation. Could you suggest a better term to contrast this with authoritarianism?