#21055 ⟨a, b | ba=ab, aaab=aab⟩
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 ⋅ a2b = a2b and a ⋅ ab = a2b, however a2b ≠ ab
- Gröbner basis: ⟨a, b | a3b=a2b⟩
- 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,aaab=aab ab - -
ba=ab
aaab=aab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
5 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 21056 | ⟨a, b | ba=ab, aaab=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 21058 | ⟨a, b | ba=ab, aaab=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 21063 | ⟨a, b | ba=ab, aaba=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 21064 | ⟨a, b | ba=ab, aaba=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 21066 | ⟨a, b | ba=ab, aaba=baa⟩ | φ(a) = a, φ(b) = b |