#21055 ⟨a, b | ba=ab, aaab=aab⟩
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- Properties
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Presentation has sum-of-sides 11
- Infinite non-cancellative commutative monoid
- Not cancellative, because multiplication by a2b2 is not injective:
-
a2b2 ⋅ a = a2b2 and a2b2 ⋅ 1 = a2b2, however a ≠ 1
- Commutative 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 |