definition 4.35 The group axioms, restated one at a time
open in the book ·
parts/02-mathematical-methods/02-algebraic-structures.tex:947
· p. 68
- ground object -- no derivation owed
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 4.3
Algebraic structure
¶
-
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 4.6
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 4.6
Associativity
¶
-
depends_on
definition 4.11
Inverse element
¶
Supports
Nothing declares a dependency on this node yet.
Neighborhood
Every logical edge within two steps of this node.
- declared and complete
- partly declared
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| type | direction | node | provenance | where |
|---|---|---|---|---|
depends_on |
→ | Group | declared | parts/02-mathematical-methods/02-algebraic-structures.tex:980 |