Finding Elements of a Quotient Ring

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SUMMARY

The discussion focuses on the method for finding elements of a quotient ring in abstract algebra. Participants emphasize that elements can be represented as p(x) + I, where p(x) is a polynomial and I is an ideal. It is recommended to choose the polynomial with the smallest degree as the representative for each element. This approach simplifies the identification of all elements within the quotient ring.

PREREQUISITES
  • Understanding of abstract algebra concepts, particularly rings and ideals.
  • Familiarity with polynomial functions and their properties.
  • Knowledge of quotient structures in algebra.
  • Basic skills in manipulating algebraic expressions.
NEXT STEPS
  • Study the properties of ideals in ring theory.
  • Learn about polynomial representation in quotient rings.
  • Explore examples of quotient rings with specific ideals.
  • Investigate the role of degree in polynomial selection for quotient elements.
USEFUL FOR

Students of abstract algebra, mathematicians exploring ring theory, and educators seeking to clarify concepts related to quotient rings.

Soccer4822
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Hello all, first time to the site and its very helpful! I wish I would have found it sooner.
I am stuck on quotient rings. Here is my question..

How do I find elements of a quotient ring?

It asks me to list all elements of a quotient ring.

Anybody have any ideas how i can find them? :confused:
 
Last edited:
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You'll have to state the question.
And by the way, I think these questions (that is, HW questions) should be asked several forums above.
 
In your quotient ring, all the elements look like p(x)+I. Now you know for a given element in the quotient ring, you can take many different p(x)'s as it's representative. Try to take the one with the smallest degree.

-I see you've edited while I was replying, so the above may look strange to others.
 

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