#21057 ⟨a, b | ba=ab, aaab=abb⟩
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 ⋅ a2b = ab2 and a ⋅ b2 = ab2, however a2b ≠ b2
- Gröbner basis: ⟨a, b | ab2=a3b⟩
- 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,aaab=abb ab - -
ba=ab
aaab=abb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
5 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 21059 | ⟨a, b | ba=ab, aaab=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 21060 | ⟨a, b | ba=ab, aaab=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 21065 | ⟨a, b | ba=ab, aaba=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 21067 | ⟨a, b | ba=ab, aaba=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 21068 | ⟨a, b | ba=ab, aaba=bba⟩ | φ(a) = a, φ(b) = b |