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2 cards from this section. Quick, good the night before a test.
Define a ring in your own words.
Think about the combination of a set and operations.
What is an example of a ring?
Consider commonly used number sets.
What are the properties required for a ring?
Recall the axioms discussed in class.
All non-zero elements in a field have an inverse.
Think about what makes fields special compared to rings.
Given a ring of integers mod 5, determine whether the number 2 has a multiplicative inverse.
Try finding a number that gives 1 when multiplied by 2.
Prove that the set of polynomials over a ring forms a ring itself.
Focus on how addition and multiplication of coefficients work in the original ring.
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