19.2.7 - Definition of a Field
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Practice Questions
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What is a field?
💡 Hint: Think about mathematical structures you have encountered.
List the three main axioms for a field.
💡 Hint: These involve operations and properties.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is required for a set to be a field?
💡 Hint: Consider the definitions of mathematical structures.
In a field, if x ∙ y = 0, what can we conclude?
💡 Hint: Review the properties of fields.
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Challenge Problems
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Prove that the set of rational numbers Q forms a field.
💡 Hint: Reference the axioms discussed.
Given a finite field constructed using Z_5, show the elements and their multiplication table.
💡 Hint: Remember to check that operations modulo 5 are preserved.
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