A ground ring (or base ring, field of scalars, etc) is a ring (usually a commutative ring or even a field) which is fixed in a given situation, such that everything takes place ‘over’ . There is no technical definition here; rather, it is the meaning of ‘over’ that must be defined in any particular case.
There are analogies between the ground ring and the base space of a bundle. There are also generalisations in which might be, for example, a monad. It is also important to consider base change from one ground ring to another, mediated by a ring homomorphism or even a bimodule.
Perhaps most fundamentally, the categories Mod and Vect depend on (respectively) a ground ring and a ground field. That is, a module is not just a module but a -module (either left or right when might not be commutative), and a vector space is not just a vector space but a vector space over . Conversely, the ground ring/field itself appears as the unit of the tensor product in these categories.
Other terms which depend on a ground ring/field include:
This list is very incomplete, made mostly by searching for ‘ground ring’, ‘base field’, etc.