#7017 ⟨a, b | ba=ab, aaaab=b⟩
Contents
- Properties
- Commutative structure
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative commutative monoid
- Element a has infinite order
- Not cancellative, because multiplication by ab is not injective:
-
ab ⋅ a4 = ab and ab ⋅ 1 = ab, however a4 ≠ 1
- Gröbner basis: ⟨a, b | a4b=b⟩
- Cancellative quotient is isomorphic to ℤ4 ⊕ ℕ
- Enveloping group is isomorphic to ℤ4 ⊕ 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=b ab - -
ba=ab
aaaab=b
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 7019 | ⟨a, b | ba=ab, aaaba=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 7023 | ⟨a, b | ba=ab, aabaa=b⟩ | φ(a) = a, φ(b) = b |