#15479 ⟨a, b | aaa=ab, baabb=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 ⋅ b = a3 and a ⋅ a2 = a3, however b ≠ a2
- Gröbner basis: ⟨a, b | a8=a, ab=a3⟩
- 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:aaa=ab,baabb=a a/b - -
aaaaaaaa=a
ba=aaa
ab=aaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 15483 | ⟨a, b | aaa=ab, babab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15485 | ⟨a, b | aaa=ab, babba=a⟩ | φ(a) = a, φ(b) = b |