#7130 ⟨a, b | ba=ab, aabb=ab⟩
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 ⋅ ab = ab and ab ⋅ 1 = ab, however ab ≠ 1
- Gröbner basis: ⟨a, b | a2b2=ab⟩
- Cancellative quotient is isomorphic to ℤ
- Enveloping group is isomorphic to 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,aabb=ab ab - -
ba=ab
aabb=ab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
4 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 7131 | ⟨a, b | ba=ab, aabb=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 7133 | ⟨a, b | ba=ab, abab=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 7134 | ⟨a, b | ba=ab, abab=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 7136 | ⟨a, b | ba=ab, abba=ab⟩ | φ(a) = a, φ(b) = b |