Death Note question(Warning:Manga ending spoiler inside)!?!?

O.K. i'm a little confused with the ending of the Manga version of the Anime series Death Note i was reading info on Death Note from wikipedia to see if Light actually creates his envisioned Utopia at the end,and it said Light dies at the end of both the Manga & Anime versions of the show,but in the Manga version he literally begs Ryuk to save his life by written both Mello & Nears' names in his(Ryuk) Death Note,but Ryuk responds to Light claiming that he is Neutral,and on neither Near & Mellos' nor Light's side of the battle,and then he says that he will do what he promised to do 9 years ago(when they first meet),and he will & did write Light's name in his Death Note,then Light dies,but here's what i'm confused about when Rem wrote L's name in her Death Note to save the life of Misa & Rem died,but when Ryuk wrote Light's name in his Death Note to save him of his pain & agony did Ryuk die or did he live,because he never truly saw Light as a friend or someone to care for?