Definition 31.26.2. Let X be a locally Noetherian integral scheme.
A prime divisor is an integral closed subscheme Z \subset X of codimension 1.
A Weil divisor is a formal sum D = \sum n_ Z Z where the sum is over prime divisors of X and the collection \{ Z \mid n_ Z \not= 0\} is locally finite (Topology, Definition 5.28.4).
The group of all Weil divisors on X is denoted \text{Div}(X).
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