#20859 ⟨a, b | ba=ab, aaabb=aa⟩
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 a is not injective:
-
a ⋅ a2b2 = a2 and a ⋅ a = a2, however a2b2 ≠ a
- Gröbner basis: ⟨a, b | a3b2=a2⟩
- Cancellative quotient is isomorphic to ℤ
- Enveloping group is isomorphic to ℤ
- Group of units is isomorphic to ℤ1
- 3 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=aa ab - -
ba=ab
aaabb=aa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
5 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 20866 | ⟨a, b | ba=ab, aabab=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20870 | ⟨a, b | ba=ab, aabba=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20874 | ⟨a, b | ba=ab, abaab=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20878 | ⟨a, b | ba=ab, ababa=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20883 | ⟨a, b | ba=ab, abbba=bb⟩ | φ(a) = b, φ(b) = a |