#7190 ⟨a, b | ba=ab, abb=aab⟩
Contents
- Properties
- Commutative structure
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative commutative monoid
- Element a has infinite order
- Not cancellative, because multiplication by ab is not injective:
-
ab ⋅ a = ab2 and ab ⋅ b = ab2, however a ≠ b
- Gröbner basis: ⟨a, b | a2b=ab2⟩
- Cancellative quotient is isomorphic to ℕ
- 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,abb=aab ab - -
ba=ab
abb=aab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 7191 | ⟨a, b | ba=ab, abb=aba⟩ | φ(a) = a, φ(b) = b |
| 10 | 7193 | ⟨a, b | ba=ab, baa=abb⟩ | φ(a) = a, φ(b) = b |
| 10 | 7195 | ⟨a, b | ba=ab, bab=aba⟩ | φ(a) = a, φ(b) = b |