Krull modules over integral domains

We define a concept of strongly Krull (s-Krull) modules over integral domains. One of the main aims is to study arithmetic properties of s-Krull modules. There are two different definitions of Krull modules over integral domains, that is: Krull modules in the sense of Costa and Johnson and Krull modules in the sense of ours. It turns out that Krull modules in the sense of Costa and Johnson imply s-Krull modules and s-Krull modules imply Krull modules in the sense of ours. The reverse of the statements do not necessarily hold