Flatness is a property of a module over a ring that signifies the module behaves well with respect to the tensor product. In simpler terms, a flat module can be thought of as one that preserves exact sequences when tensored with other modules, which means it does not introduce any new relations or dependencies. This concept is crucial in various areas of algebraic K-theory, particularly in understanding the localization sequence, where flatness helps manage how modules interact under localization.
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