#2211 ⟨a, b | ba=ab, aaab=b⟩
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- Properties
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Presentation has sum-of-sides 9
- Infinite non-cancellative commutative monoid
- Not cancellative, because multiplication by ab is not injective:
-
ab ⋅ a3 = ab and ab ⋅ 1 = ab, however a3 ≠ 1
- Commutative Gröbner basis: ⟨a, b | a3b=b⟩
- Cancellative quotient is isomorphic to ℤ3 ⊕ ℕ
- Enveloping group is isomorphic to ℤ3 ⊕ 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,aaab=b ab
ba=ab
aaab=b
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
6 total
| Σ | # | Presentation | Mapping |
|---|
| 9 | 2213 | ⟨a, b | ba=ab, aaba=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 4676 | ⟨a, b | aaab=b, aaba=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 4718 | ⟨a, b | aaba=b, abaa=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 12935 | ⟨a, b | aba=aab, aaab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 12937 | ⟨a, b | aba=aab, aaba=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 12941 | ⟨a, b | aba=aab, abaa=b⟩ | φ(a) = a, φ(b) = b |