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2 cards from this section. Quick, good the night before a test.
What is a ring?
Think of a set of numbers and how operations can be performed on them.
Define an abelian group.
Consider how the order of operations affects the result.
What are the three main axioms defining a ring?
Recall the definition discussed in class.
True or False: Every element in a ring has a multiplicative inverse.
Think about the examples presented regarding invertible elements.
Prove that the integers modulo 6, Z₆, with defined addition and multiplication modulo 6 form a ring. Provide a thorough explanation for each axiom.
Use specific examples within the set for your proof.
Using the concept of co-primality, discuss how the integers modulo 15 demonstrate which elements are invertible.
Find the gcd with 15 for various elements.
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