#21071 ⟨a, b | ba=ab, aabb=aab⟩
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 a2b is not injective:
-
a2b ⋅ b = a2b and a2b ⋅ 1 = a2b, however b ≠ 1
- Gröbner basis: ⟨a, b | a2b2=a2b⟩
- Cancellative quotient is isomorphic to ℕ
- 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=aab ab - -
ba=ab
aabb=aab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
9 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 21072 | ⟨a, b | ba=ab, aabb=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 21073 | ⟨a, b | ba=ab, aabb=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 21075 | ⟨a, b | ba=ab, abab=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 21076 | ⟨a, b | ba=ab, abab=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 21077 | ⟨a, b | ba=ab, abab=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 21079 | ⟨a, b | ba=ab, abba=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 21080 | ⟨a, b | ba=ab, abba=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 21081 | ⟨a, b | ba=ab, abba=abb⟩ | φ(a) = b, φ(b) = a |
| 11 | 21082 | ⟨a, b | ba=ab, abba=bab⟩ | φ(a) = b, φ(b) = a |