Is Korea "a part of China" in the same way the PRC claims Taiwan and Tibet?

China was responsible for helping their ally, the North Korea. They are responsible for splitting up the two Korea's by siding with North in attacking the South. To this day, North Korea is still China's biggest ally, this means the tendency of China to make claims on Korea will be stronger and soon it will be concluded into children's textbooks that Korea is part of China already.