#20852 ⟨a, b | ba=ab, aaaab=ab⟩
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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 ⋅ a3 = ab and ab ⋅ 1 = ab, however a3 ≠ 1
- Commutative Gröbner basis: ⟨a, b | a4b=ab⟩
- Cancellative quotient is isomorphic to ℤ3 ⊕ ℕ
- Enveloping group is isomorphic to ℤ3 ⊕ 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,aaaab=ab ab
ba=ab
aaaab=ab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
4 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 20853 | ⟨a, b | ba=ab, aaaab=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 20856 | ⟨a, b | ba=ab, aaaba=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20857 | ⟨a, b | ba=ab, aaaba=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 20864 | ⟨a, b | ba=ab, aabaa=ab⟩ | φ(a) = a, φ(b) = b |