A commutative unit ring R (with the multiplicative neutral element 1) is called a field, if R is not the zero ring and every element x\in R with x\neq 0 (0 being the additive neutral element) has a multiplicative inverse. "Unfolding" all definitions, a field fulfills the following axioms:
Algorithms: 1
Branches: 2
Chapters: 3 4 5 6 7
Corollaries: 8 9
Definitions: 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46
Examples: 47 48
Explanations: 49
Lemmas: 50
Proofs: 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
Propositions: 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90
Theorems: 91 92 93 94