#20860 ⟨a, b | ba=ab, aaabb=ab⟩
Contents
- Properties
- Commutative structure
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative commutative monoid
- Element a has infinite order
- Not cancellative, because multiplication by ab is not injective:
-
ab ⋅ a2b = ab and ab ⋅ 1 = ab, however a2b ≠ 1
- Gröbner basis: ⟨a, b | a3b2=ab⟩
- Cancellative quotient is isomorphic to ℤ
- Enveloping group is isomorphic to ℤ
- Group of units is isomorphic to ℤ1
- 4 Archimedian components:
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ba=ab,aaabb=ab ab - -
ba=ab
aaabb=ab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
9 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 20861 | ⟨a, b | ba=ab, aaabb=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 20867 | ⟨a, b | ba=ab, aabab=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20868 | ⟨a, b | ba=ab, aabab=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 20871 | ⟨a, b | ba=ab, aabba=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20872 | ⟨a, b | ba=ab, aabba=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 20875 | ⟨a, b | ba=ab, abaab=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20876 | ⟨a, b | ba=ab, abaab=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 20879 | ⟨a, b | ba=ab, ababa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20882 | ⟨a, b | ba=ab, abbba=ab⟩ | φ(a) = b, φ(b) = a |