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CSET: Fields/Rings

What is the written definition of a field? A field is a commutative ring with unity in which every nonzero element is a unit.
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+
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.
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
What is the list definition of a field? 1. Is a ring 2. Has multiplicative identity / multiplicative inverse 3. Multiplication is commutative (abelian)
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
What is the difference between a commutative ring and a ring? A commutative ring is abelian for addition AND multiplication
Created by: ok2bpure