Multiplicative functions and homomorphisms

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Homework Help Overview

The discussion revolves around the concepts of multiplicative functions and homomorphisms, exploring their definitions and differences in a mathematical context.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants attempt to define multiplicative functions and homomorphisms, noting the relationship between their properties. Questions arise regarding the clarity and mathematical rigor of the term "preserve structure."

Discussion Status

The discussion is ongoing, with participants examining the definitions and implications of the terms involved. Some guidance has been offered regarding the nature of homomorphisms in relation to rings, but there is no explicit consensus on the definitions or interpretations yet.

Contextual Notes

There appears to be a concern about the subjective nature of certain expressions used in the definitions, prompting further inquiry into their mathematical meaning.

ehrenfest
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Homework Statement


What is the difference between multiplicative functions and homomorphisms?


Homework Equations





The Attempt at a Solution

 
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Multiplicative functions: the product of the image is the image of the product. There is another definition requiring that the two elements must be relatively prime.

Homomorphisms: preserve structure between the domain and the codomain, this often requires a homomorphism to be multiplicative.
 
I don't like that expression "preserve structure between the domain and the codomain" because it seems like it is not mathematical or even objective...

What does that mean in mathematical terms?
 
In rings it means that multiplication and addition in each ring are very similar.
 

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