Rev., more correctly, ye died; the aorist tense indicating a definite event. Paul uses the word died in many different relations, expressing that with which death dissolves the connection. Thus, died unto sin, unto self, unto the law, unto the world.
Rudiments of the world
Elementary teachings and practices the peculiar sphere of which is the world. World (κόσμου) has its ethical sense, the sum-total of human life in the ordered world, considered apart from, alienated from, and hostile to God, and of the earthly things which seduce from God. See on Joh 1:9.
Are ye subject to ordinances (δογματίζεσθε)
Only here in the New Testament. Rev., subject yourselves. Better passive, as emphasizing spiritual bondage. Why do ye submit to be dictated to? See on 1Co 1:22, where the imperious attitude of the Jews appears in their demanding credentials of the Gospel as sole possessors of the truth. The ordinances include both those of the law and of philosophy.