Search engines are among the most important applications or services on the web. Most existing successful search engines use global ranking algorithms to generate the ranking of documents crawled in their databases. However, global ranking of documents has two potential problems: high computation cost and potentially poor rankings. Both of the problems are related to the centralized computation paradigm. We propose to decentralize the task of ranking. This requires two things: a decentralized architecture and a logical framework for ranking computation. In the paper we introduce a ranking algebra providing such a formal framework. Through partitioning and combining rankings, we manage to compute document rankings of large-scale web data sets in a localized fashion. We provide initial results, demonstrating that the use of such an approach can ameliorate the above-mentioned problems. The approach presents a step towards P2P Web search engines.