proposition 4.25 Neutral element equal to a product

open in the book · parts/02-mathematical-methods/02-algebraic-structures.tex:634 · p. 64

Rests on

depends_on definition 4.21 Group ¶
- depends_on definition 4.11 Inverse element ¶
  - depends_on definition 4.9 Neutral element ¶
    - depends_on definition 4.3 Algebraic structure ¶
      - depends_on definition 4.2 Binary operation ¶
- 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 4.3 Algebraic structure ¶ ↺
    - depends_on definition 4.4 Internal binary operation; magma ¶
      - depends_on definition 4.3 Algebraic structure ¶ ↺
      - depends_on definition 4.2 Binary operation ¶ ↺
proves proof ch:02-algebraic-structures@proof-6 ¶

Supports

depends_on proposition 4.26 Involution of the inverse ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Group	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:643
`depends_on`	←	Involution of the inverse	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:663
`proves`	←	ch:02-algebraic-structures@proof-6	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:646