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2 cards from this section. Quick, good the night before a test.
What is a field?
Think about mathematical structures you have encountered.
List the three main axioms for a field.
These involve operations and properties.
What is required for a set to be a field?
Consider the definitions of mathematical structures.
In a field, if x ∙ y = 0, what can we conclude?
Review the properties of fields.
Prove that the set of rational numbers Q forms a field.
Reference the axioms discussed.
Given a finite field constructed using Z_5, show the elements and their multiplication table.
Remember to check that operations modulo 5 are preserved.
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