The Buddhist kingdom in Beijiang centered around Turfan was the only area where the people were identified as "Uyghurs" after the Islamic invasions. The broader Turfan area was bordered by Nanjiang to the west, the Tian Shan to the north, the Kunlun Shan to the south, and the principality of Hami. In 1513 Hami became a dependency of Turfan and remained so until the end of Moghul rule. As a result, the Moghuls became direct neighbors of Ming China. Although the term "Uyghurstan" was used for the Turfan city-state, the term is confused in Muslim sources with Cathay. The Uyghur khans had voluntarily become Mongol vassals during the reign of Genghis Khan and as a result were allowed to retain their territories. As the Mongol Empire was split up in the middle of the 13th century, the Xinjiang region was assigned to the Chagatayids. The power of the Uyghur khans slowly declined under Mongol rule until the last recorded khan was forcibly converted to Islam in the 1380s or 90s. After the 15th century it seems to have been subjected to direct Moghul rule, and a separate Moghul Khanate was established there in mid-15th century. After the Islamization of Turfan, the non-Islamic term "Uyghur" would disappear until the Chinese Nationalist leader Sheng Shicai, following the Soviet Union, introduced it for a different, Muslim population in 1934.