  We show that the theory of quantales and quantic nuclei motivate new results
on star operations, semistar operations, semiprime operations, ideal systems,
and module systems, and conversely the latter theories motivate new results on
quantales and quantic nuclei. Results include representation theorems for
precoherent prequantales and multiplicative semilattices; characterizations of
the simple prequantales; and a generalization to the setting of precoherent
quantales of the construction of the largest finite type semistar operation and
the largest stable semistar operation smaller than a given semistar operation.
