  We study maximally entangled states and fully entangled fraction in general
d'\otimes d (d'\geq d) systems. Necessary and sufficient conditions for
maximally entangled pure and mixed states are presented. As a natural
generalization of the usual fully entangled fraction for d\otimes d systems, we
define the maximal overlap between a given quantum state and the maximally
entangled states as the fully entangled fraction in d'\otimes d systems. The
properties of this fully entangled fraction and its relations to quantum
teleportation have been analyzed. The witness for detecting maximally entangled
states and quantum states that are useful for quantum teleportation is
provided.
