(Just so you know) this article was started by merging Localization of a ring and Localization of a module. The hope is that when it became mature we redirect these 2 articles to this one. As of writing this, the article still needs more work that is required when articles are merged. -- Taku (talk) 19:11, 10 March 2012 (UTC)
About "local property". I'm having very hard time writing that section. (I don't mind if anyone else writes it.) After googling and reading standard textbooks, I couldn't reach a definitive conclusion. Some (notably Atiyah-Macdonald) defines local property w.r.t. prime ideals "but" used it to mean "local property" w.r.t. max ideals. (I usually find Eisenbud confusing and thus didn't look it up.) -- Taku (talk) 23:32, 12 March 2012 (UTC)