definition 4.62 Cosets
open in the book ·
parts/02-mathematical-methods/02-algebraic-structures.tex:2148
· p. 84
- ground object -- no derivation owed
Rests on
-
depends_on
definition 3.59
Equivalence class
¶
- depends_on definition 3.58 Equivalence relation ¶
-
depends_on
proposition 4.61
prop:alg-coset-equiv
¶
-
depends_on
definition 4.36
Subgroup
¶
-
depends_on
definition 4.21
Group
¶
-
depends_on
definition 4.11
Inverse element
¶
- depends_on definition 4.9 Neutral element ¶
-
depends_on
definition 4.20
Monoid
¶
- depends_on definition 4.9 Neutral element ¶ ↺
- depends_on definition 4.18 Semigroup ¶
-
depends_on
definition 4.11
Inverse element
¶
-
depends_on
definition 4.21
Group
¶
- depends_on definition 3.58 Equivalence relation ¶ ↺
- proves proof ch:02-algebraic-structures@proof-21 ¶
-
depends_on
definition 4.36
Subgroup
¶
Supports
- depends_on proposition 4.63 Well-definedness of the coset product ¶
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 |
→ | Equivalence class | declared | parts/02-mathematical-methods/02-algebraic-structures.tex:2161 |
depends_on |
→ | prop:alg-coset-equiv | declared | parts/02-mathematical-methods/02-algebraic-structures.tex:2161 |
depends_on |
← | Well-definedness of the coset product | declared | parts/02-mathematical-methods/02-algebraic-structures.tex:2277 |