#7122 ⟨a, b | ba=ab, aaab=ab⟩
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 ab is not injective:
-
ab ⋅ a2 = ab and ab ⋅ 1 = ab, however a2 ≠ 1
- Commutative Gröbner basis: ⟨a, b | a3b=ab⟩
- Cancellative quotient is isomorphic to ℤ2 ⊕ ℕ
- Enveloping group is isomorphic to ℤ2 ⊕ ℤ
- Group of units is isomorphic to ℤ1
- 4 Archimedian components:
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ba=ab,aaab=ab ab
ba=ab
aaab=ab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 7123 | ⟨a, b | ba=ab, aaab=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 7126 | ⟨a, b | ba=ab, aaba=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 7127 | ⟨a, b | ba=ab, aaba=ba⟩ | φ(a) = a, φ(b) = b |