#2264 ⟨a, b | ba=ab, aab=ab⟩
Contents
- Properties
- Commutative structure
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 9
- Infinite non-cancellative commutative monoid
- Element a has infinite order
- Not cancellative, because multiplication by ab is not injective:
-
ab ⋅ a = ab and ab ⋅ 1 = ab, however a ≠ 1
- Gröbner basis: ⟨a, b | a2b=ab⟩
- 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,aab=ab ab - -
ba=ab
aab=ab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
4 total
| Σ | # | Presentation | Mapping |
|---|
| 9 | 2265 | ⟨a, b | ba=ab, aab=ba⟩ | φ(a) = a, φ(b) = b |
| 9 | 2268 | ⟨a, b | ba=ab, aba=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 16151 | ⟨a, b | aab=ab, aaab=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 16391 | ⟨a, b | aba=ab, abaa=ba⟩ | φ(a) = a, φ(b) = b |