#6364 ⟨a, b | aab=a, babbb=a⟩
Contents
- Properties
- Commutative structure
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative commutative monoid
- Element b has infinite order
- Not cancellative, because multiplication by a is not injective:
-
a ⋅ b4 = a and a ⋅ 1 = a, however b4 ≠ 1
- Gröbner basis: ⟨a, b | a5=a, ab=a4⟩
- Cancellative quotient is isomorphic to ℤ4
- Enveloping group is isomorphic to ℤ4
- Group of units is isomorphic to ℤ1
- 3 Archimedian components:
- Reduction order:
- Left-to-right recursive path with deg(b) = 0; deg(a) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aab=a,babbb=a b/a - -
abbbb=a
ba=ab
aa=abbb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
4 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 6600 | ⟨a, b | aab=a, aaaa=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 6642 | ⟨a, b | aab=a, babb=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 6812 | ⟨a, b | aab=a, bab=aaa⟩ | φ(a) = a, φ(b) = b |
| 10 | 6830 | ⟨a, b | aba=a, bab=aaa⟩ | φ(a) = a, φ(b) = b |