#240 ⟨a, b | aa=a, aba=b⟩
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- Properties
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Presentation has sum-of-sides 7
- Infinite non-cancellative commutative monoid
- Not cancellative, because multiplication by b is not injective:
-
b ⋅ a = b and b ⋅ 1 = b, however a ≠ 1
- Commutative Gröbner basis: ⟨a, b | a2=a, ab=b⟩
- Cancellative quotient is isomorphic to ℕ
- Enveloping group is isomorphic to 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:aa=a,aba=b ab
aa=a
ab=b
ba=b
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
8 total
| Σ | # | Presentation | Mapping |
|---|
| 8 | 885 | ⟨a, b | aa=a, aaba=b⟩ | φ(a) = a, φ(b) = b |
| 9 | 2861 | ⟨a, b | aa=a, aaaba=b⟩ | φ(a) = a, φ(b) = b |
| 9 | 2865 | ⟨a, b | aa=a, aabaa=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 8573 | ⟨a, b | aa=a, aaaaba=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 8577 | ⟨a, b | aa=a, aaabaa=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 24049 | ⟨a, b | aa=a, aaaaaba=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 24053 | ⟨a, b | aa=a, aaaabaa=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 24061 | ⟨a, b | aa=a, aaabaaa=b⟩ | φ(a) = a, φ(b) = b |