In recent years there has been a significant interest in peer-to-peer (P2P) environments in the community ofdata management. However, almost all work, so far, is focused on exact query processing in current P2P data systems.The autonomy of peers also is not considered enough. In addition, the system cost is very high because the informationpublishing method of shared data is based on each document instead of document set. In this paper, abstract indices (AbIx)are presented to implement content-based approximate queries in centralized, distributed and structured P2P data systems.It can be used to search as few peers as possible but get as many returns satisfying users queries as possible on the guaranteeof high autonomy of peers. Also, abstract indices have low system cost, can improve the query processing speed, and supportvery frequent updates and the set information publishing method. In order to verify the effectiveness of abstract indices, asimulator of 10,000 peers, over 3 million documents is made, and several metrics are proposed. The experimental results showthat abstract indices work well in various P2P data systems.