proposition 4.40 prop:alg-congruence-equiv

open in the book · parts/02-mathematical-methods/02-algebraic-structures.tex:1278 · p. 72

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 ¶ ↺
depends_on definition 3.58 Equivalence relation ¶
proves proof ch:02-algebraic-structures@proof-10 ¶

Supports

depends_on proposition 4.41 prop:alg-zn-group ¶
- depends_on example 4.69 The Cayley table of $\Z_2\times\Z_4$ ¶

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:1280
`depends_on`	→	Equivalence relation	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:1280
`depends_on`	←	prop:alg-zn-group	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:1359
`proves`	←	ch:02-algebraic-structures@proof-10	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:1283