#8776 ⟨a, b | ab=a, baaaaa=a⟩
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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 a is not injective:
-
a ⋅ b = a and a ⋅ 1 = a, however b ≠ 1
- Commutative Gröbner basis: ⟨a, b | ab=a, 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=a,baaaaa=a ab
ab=a
ba=a
aaaaa=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
6 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 24462 | ⟨a, b | ab=a, baaaaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24464 | ⟨a, b | ab=a, baaaaba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24468 | ⟨a, b | ab=a, baaabaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24476 | ⟨a, b | ab=a, baabaaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24492 | ⟨a, b | ab=a, babaaaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24989 | ⟨a, b | ab=a, baaaaa=ab⟩ | φ(a) = a, φ(b) = b |