This paper presents the achievable rate region frontiers for the n-user interference channel when there is no cooperation at the transmit nor at the receive side. The receiver is assumed to treat the interference as additive thermal noise and does not employ multiuser detection. In this case, the rate region frontier for the n-user interference channel is found to be the union of n hyper-surface frontiers of dimension n-1, where each is characterized by having one of the transmitters transmitting at full power. The paper also finds the conditions determining the convexity or concavity of the frontiers for the case of twouser interference channel, and discusses when a time sharing approach should be employed with specific results pertaining to the two-user symmetric channel.