#8630 ⟨a, b | aa=a, babbab=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 ⋅ a = a and a ⋅ 1 = a, however a ≠ 1
- Gröbner basis: ⟨a, b | a2=a, ab4=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:aa=a,babbab=a ab - -
aa=a
ba=ab
abbbb=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
6 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 15719 | ⟨a, b | aab=ba, babbb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15731 | ⟨a, b | aab=ba, bbbab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15887 | ⟨a, b | aba=ab, babbb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24160 | ⟨a, b | aa=a, baabbab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24166 | ⟨a, b | aa=a, bababab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24707 | ⟨a, b | aa=a, babbab=aa⟩ | φ(a) = a, φ(b) = b |