  In this paper, we first consider the relationship between a polynomial ring
$B$ over a Noetherian domain $R$ and the ring of invariants $A$ of a ${\mathbb
G}_a$-action on $B$, when $A$ occurs as a retract of $B$. Next, we study
retracts of a polynomial ring in general and address the questions of D. L.
Costa raised in \cite{C}. Finally, we examine the behaviour of ideals and
certain properties of rings under retractions.
