#18926 ⟨a, b | aab=a, babbbb=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 ⋅ b5 = a and a ⋅ 1 = a, however b5 ≠ 1
- Gröbner basis: ⟨a, b | a6=a, ab=a5⟩
- Cancellative quotient is isomorphic to ℤ5
- Enveloping group is isomorphic to ℤ5
- Group of units is isomorphic to ℤ1
- 3 Archimedian components:
- Reduction order:
- Left-to-right recursive path with deg(b) = 0; deg(a) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aab=a,babbbb=a b/a - -
abbbbb=a
ba=ab
aa=abbbb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
5 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 19378 | ⟨a, b | aab=a, aaaaa=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 19468 | ⟨a, b | aab=a, babbb=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 19925 | ⟨a, b | aab=a, aaaa=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20008 | ⟨a, b | aab=a, babb=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20180 | ⟨a, b | aba=a, aaaa=bab⟩ | φ(a) = a, φ(b) = b |