#14357 ⟨a, b | aaaa=a, baaab=a⟩
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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 ab is not injective:
-
ab ⋅ b2 = a2b and ab ⋅ a = a2b, however b2 ≠ a
- Commutative Gröbner basis: ⟨a, b | ab2=a2, a4=a⟩
- Cancellative quotient is isomorphic to ℤ6
- Enveloping group is isomorphic to ℤ6
- 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:aaaa=a,baaab=a ab
ba=ab
abb=aa
aaaa=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
5 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 15766 | ⟨a, b | aab=bb, abbba=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 15920 | ⟨a, b | aba=bb, aabbb=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 15928 | ⟨a, b | aba=bb, abbab=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 15930 | ⟨a, b | aba=bb, abbba=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 15936 | ⟨a, b | aba=bb, baabb=b⟩ | φ(a) = b, φ(b) = a |