#20851 ⟨a, b | ba=ab, aaaab=aa⟩
Contents
- Properties
- Commutative structure
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative commutative monoid
- Element a has infinite order
- Not cancellative, because multiplication by a is not injective:
-
a ⋅ a3b = a2 and a ⋅ a = a2, however a3b ≠ a
- Gröbner basis: ⟨a, b | a4b=a2⟩
- Cancellative quotient is isomorphic to ℤ
- Enveloping group is isomorphic to ℤ
- 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:ba=ab,aaaab=aa ab - -
ba=ab
aaaab=aa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 20855 | ⟨a, b | ba=ab, aaaba=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20863 | ⟨a, b | ba=ab, aabaa=aa⟩ | φ(a) = a, φ(b) = b |