#7189 ⟨a, b | ba=ab, abb=aaa⟩
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- Properties
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Presentation has sum-of-sides 10
- Infinite non-cancellative commutative monoid
- Not cancellative, because multiplication by ab is not injective:
-
ab ⋅ a2 = a3b and ab ⋅ b2 = a3b, however a2 ≠ b2
- Commutative Gröbner basis: ⟨a, b | ab2=a3⟩
- Enveloping group is isomorphic to ℤ2 ⊕ 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,abb=aaa ab
ba=ab
abb=aaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 7194 | ⟨a, b | ba=ab, bab=aaa⟩ | φ(a) = a, φ(b) = b |