CSET: Fields/Rings
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| What is the written definition of a field? | A field is a commutative ring with unity in which every nonzero element is a unit.
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| What is the written definition of an ordered field? | A field F is orderable if it has a subset F+ such that F+ is also closed under addition/multiplication and that for any element in F, its unit is in F+
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| What is the written definition of a ring? | A set with two binary operations: addition and multiplication, provided that the set is abelian under addition, that multiplication is associative, and that both the distributive laws hold for all elements of the set.
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| What is the 4 point definition of a ring? | 1. Addition is commutative
2. Add/Mult are associative
3. There is an additive identity / additive inverse
4. Distributive laws hold
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| What is the list definition of a field? | 1. Is a ring
2. Has multiplicative identity / multiplicative inverse
3. Multiplication is commutative (abelian)
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| What is the list definition of an ordered field? | 1. A field
2. A Set
3. Has a subset
4. The subset contains the additive/multiplicative inverses
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| What is the difference between a commutative ring and a ring? | A commutative ring is abelian for addition AND multiplication
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