In algebra, the concept of **change of rings** involves the study of a ring homomorphism and how it allows us to transfer structures and properties from one ring to another. This is particularly relevant in areas like algebraic geometry, representation theory, and commutative algebra.
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Changing the coefficient ring of a module along a ring homomorphism can mean restriction of scalars, extension of scalars, or coextension of scalars. The underlying module may be retained with a smaller ring action, or replaced by a tensor or Hom construction with the new ring.