  We study the algebraic and arithmetic structure of monoids of invertible
ideals (more precisely, of $r$-invertible $r$-ideals for certain ideal systems
$r$) of Krull and weakly Krull Mori domains. We also investigate monoids of all
nonzero ideals of polynomial rings with at least two indeterminates over
noetherian domains. Among others, we show that they are not transfer Krull but
they share several arithmetical phenomena with Krull monoids having infinite
class group and prime divisors in all classes.
