#12288 ⟨a, b | aaab=ba, babb=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 ⋅ a2 = ab and ab ⋅ 1 = ab, however a2 ≠ 1
- Commutative Gröbner basis: ⟨a, b | a3=a, ab3=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:aaab=ba,babb=a ab
ba=ab
aaa=a
abbb=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
5 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 12292 | ⟨a, b | aaab=ba, bbab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12368 | ⟨a, b | aaba=ab, babb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12398 | ⟨a, b | aaba=ba, bbab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 18744 | ⟨a, b | aaa=a, baabab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 19291 | ⟨a, b | aaa=a, babab=aa⟩ | φ(a) = a, φ(b) = b |