The main purposes of this paper are to investigate Z-injective rings w
ith the representation extension property and its dual, to give a nece
ssary and sufficient condition for a Z-injective ring to be an amalgam
ation base in the class of all rings and to determine structure of Z-i
njective Noetherian rings which are amalgamation bases. Further, in th
e class of all commutative rings, it is shown that a commutative ring
has the representation extension property, if, and only if, it is an a
malgamation base.