#6982 ⟨a, b | ab=aa, baaaa=a⟩
Quick links
- Properties
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Presentation has sum-of-sides 10
- Infinite non-cancellative commutative monoid
- Not cancellative, because multiplication by a2 is not injective:
-
a2 ⋅ a = a3 and a2 ⋅ b = a3, however a ≠ b
- Commutative Gröbner basis: ⟨a, b | ab=a2, a5=a⟩
- Cancellative quotient is isomorphic to ℤ4
- Enveloping group is isomorphic to ℤ4
- 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:ab=aa,baaaa=a ab
ab=aa
ba=aa
aaaaa=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
7 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 6984 | ⟨a, b | ab=aa, baaab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6986 | ⟨a, b | ab=aa, baaba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6988 | ⟨a, b | ab=aa, baabb=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6990 | ⟨a, b | ab=aa, babaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6992 | ⟨a, b | ab=aa, babab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6994 | ⟨a, b | ab=aa, babba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6996 | ⟨a, b | ab=aa, babbb=a⟩ | φ(a) = a, φ(b) = b |