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# CSET: Fields/Rings

Question | Answer |
---|---|

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 |