proposition 4.46 Image of the neutral element

open in the book · parts/02-mathematical-methods/02-algebraic-structures.tex:1591 · p. 77

Rests on

depends_on definition 4.43 Group homomorphism ¶
- 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 4.20 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 3.43 Map ¶
  - depends_on definition 3.24 Quantifiers ¶
    - depends_on definition 3.23 Predicate ¶
      - depends_on definition 3.1 Logical proposition ¶
      - depends_on definition 3.38 Ordered pair and Cartesian product ¶
  - depends_on definition 3.28 Set ¶
proves proof ch:02-algebraic-structures@proof-13 ¶

Supports

depends_on proposition 4.47 Image of the inverse element ¶

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 homomorphism	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:1597
`depends_on`	←	Image of the inverse element	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:1618
`proves`	←	ch:02-algebraic-structures@proof-13	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:1600