#6982 ⟨a, b | ab=aa, baaaa=a⟩
Contents
- Properties
- Commutative structure
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative commutative monoid
- Element b has infinite order
- Not cancellative, because multiplication by a is not injective:
-
a ⋅ b = a2 and a ⋅ a = a2, however b ≠ a
- Gröbner basis: ⟨a, b | ab=a2, a5=a⟩
- Cancellative quotient is isomorphic to ℤ4
- Enveloping group is isomorphic to ℤ4
- 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:ab=aa,baaaa=a ab - -
ab=aa
ba=aa
aaaaa=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
7 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 6984 | ⟨a, b | ab=aa, baaab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6986 | ⟨a, b | ab=aa, baaba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6988 | ⟨a, b | ab=aa, baabb=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6990 | ⟨a, b | ab=aa, babaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6992 | ⟨a, b | ab=aa, babab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6994 | ⟨a, b | ab=aa, babba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6996 | ⟨a, b | ab=aa, babbb=a⟩ | φ(a) = a, φ(b) = b |