#1579 ⟨a, b | aaa=aa, aba=b⟩
Contents
- Properties
- Commutative structure
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 9
- Infinite non-cancellative commutative monoid
- Element b has infinite order
- Not cancellative, because multiplication by b is not injective:
-
b ⋅ a = b and b ⋅ 1 = b, however a ≠ 1
- Gröbner basis: ⟨a, b | ab=b, a3=a2⟩
- Cancellative quotient is isomorphic to ℕ
- Enveloping group is isomorphic to 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:aaa=aa,aba=b ab - -
ab=b
ba=b
aaa=aa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 5027 | ⟨a, b | aaa=aa, aaba=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15406 | ⟨a, b | aaa=aa, aaaba=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15410 | ⟨a, b | aaa=aa, aabaa=b⟩ | φ(a) = a, φ(b) = b |