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Each ''R''[''G'']-module naturally gives rise to an ''F''[''G'']-module, and, by a process often known informally as '''reduction (mod ''p'')''',
to a ''K''[''G'']-module. On the other hand, since ''R'' is a [[principal ideal ___domain]], each finite-dimensional ''F''[''G'']-module
arises by extension of scalars from an ''R''[''G'']-module.{{citation needed|date=August 2024}} In general, however, not all ''K''[''G'']-modules arise as reductions (mod ''p'') of
''R''[''G'']-modules. Those that do are '''liftable'''.
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