#12182 ⟨a, b | aaaa=ab, baab=a⟩
Contents
- Properties
- Commutative structure
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative commutative monoid
- Element b has infinite order
- Not cancellative, because multiplication by a is not injective:
-
a ⋅ a7 = a and a ⋅ 1 = a, however a7 ≠ 1
- Gröbner basis: ⟨a, b | a8=a, ab=a4⟩
- Cancellative quotient is isomorphic to ℤ7
- Enveloping group is isomorphic to ℤ7
- Group of units is isomorphic to ℤ1
- 3 Archimedian components:
- Reduction order:
- Left-to-right recursive path with deg(a) = 0; deg(b) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aaaa=ab,baab=a a/b - -
aaaaaaaa=a
ba=aaaa
ab=aaaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 12184 | ⟨a, b | aaaa=ab, baba=a⟩ | φ(a) = a, φ(b) = b |