The company's latest cell phone has no 'rival/rivals'. [=the company's newest cell phone is much better than all others available]
The company's paper is the 'rival' of any in the world. [=it is as good as any paper in the world]
He told a 'rival' version of the story. [=a version that disagrees with another version]
(..) Their abiding aim was to conquer England... then a series of petty kingdoms... each one the jealous rival of the next. Thus, when the Vikings set forth to rob and plunder England... they never sailed out of sight of land. They confined their attacks (..)1958 The Vikings