An induced homomorphism is a function between two algebraic structures that arises from a given homomorphism between two other structures, often reflecting a mapping of elements that respects the operations of those structures. In the context of ideals and quotient rings, this concept is crucial because it allows us to understand how properties of a ring can be transferred when considering its quotient with respect to an ideal. This means that if we have a ring and an ideal, we can create a new structure and still relate it back to the original through induced homomorphisms.
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