definition 4.34 Algebra

open in the book · parts/02-mathematical-methods/02-algebraic-structures.tex:863 · p. 67

ground object -- no derivation owed

Rests on

depends_on definition 4.28 Distributivity ¶
- depends_on definition 4.3 Algebraic structure ¶
  - depends_on definition 4.2 Binary operation ¶
    - depends_on definition 4.1 Cartesian product ¶
      - depends_on definition 3.28 Set ¶
    - depends_on definition 3.43 Map ¶
      - depends_on definition 3.24 Quantifiers ¶
      - depends_on definition 3.28 Set ¶ ↺
depends_on definition 4.4 Internal binary operation; magma ¶
- depends_on definition 4.3 Algebraic structure ¶ ↺
- depends_on definition 4.2 Binary operation ¶ ↺
depends_on definition 4.33 Vector space ¶
- depends_on definition 4.8 Commutativity; abelian structure ¶
  - depends_on definition 4.4 Internal binary operation; magma ¶ ↺
- depends_on definition 4.32 Field ¶
  - depends_on definition 4.11 Inverse element ¶
    - depends_on definition 4.9 Neutral element ¶
      - depends_on definition 4.3 Algebraic structure ¶ ↺
  - depends_on definition 4.20 Monoid ¶
    - depends_on definition 4.9 Neutral element ¶ ↺
    - depends_on definition 4.18 Semigroup ¶
      - depends_on definition 4.6 Associativity ¶
      - depends_on definition 4.4 Internal binary operation; magma ¶ ↺
  - depends_on definition 4.30 Ring ¶
    - depends_on definition 4.8 Commutativity; abelian structure ¶ ↺
    - depends_on definition 4.28 Distributivity ¶ ↺
    - depends_on definition 4.21 Group ¶
      - depends_on definition 4.11 Inverse element ¶ ↺
      - depends_on definition 4.20 Monoid ¶ ↺
    - depends_on definition 4.18 Semigroup ¶ ↺
- depends_on definition 4.31 Module ¶
  - depends_on definition 4.29 Action ¶
    - depends_on definition 4.9 Neutral element ¶ ↺
  - depends_on definition 4.28 Distributivity ¶ ↺
  - depends_on definition 4.21 Group ¶ ↺
  - depends_on definition 4.30 Ring ¶ ↺

Supports

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Edges

type	direction	node	provenance	where
`depends_on`	→	Distributivity	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:882
`depends_on`	→	Internal binary operation; magma	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:882
`depends_on`	→	Vector space	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:882