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What is an algebraic ring?

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Could you please break down what is an algebraic ring? I need this explained in laymans terms so that I will understand.

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https://brainmass.com/math/ring-theory/algebraic-ring-330501

Solution Preview

Since you want the answer in layman's terms, I will take an example first and then tell you what is a ring.
Consider the set of integers: Z = {..., -2, -1, 0, 1, 2, ...}
(a) If we add any two numbers of Z, we get a number which also belongs to Z (This is called Closure property under +)
(b) Let us take 3, 6, 8
(3 + 6) + 8 = 17 = 3 + (6 + 8)
This is true for any three numbers taken from Z (This is called Associative property ...

Solution Summary

Algebraic ring are broken down. Layman terms are used to understand. A complete, neat and step-by-step solution is provided in the attached file.

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