  We call a semigroup $S$ right noetherian if it satisfies the ascending chain
condition on right ideals, and we say that $S$ satisfies ACCPR if it satisfies
the ascending chain condition on principal right ideals. We investigate the
behavior of these two conditions with respect to ideals and ideal extensions,
with a particular focus on minimal and 0-minimal one-sided ideals. In
particular, we show that the property of satisfying ACCPR is inherited by right
and left ideals. On the other hand, we exhibit an example of a right noetherian
semigroup with a minimal ideal that is not right noetherian.
