#586 ⟨a, b | aab=a, baa=a⟩
Contents
- Properties
- Commutative structure
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 8
- Infinite non-cancellative commutative monoid
- Element a has infinite order
- Not cancellative, because multiplication by a is not injective:
-
a ⋅ ab = a and a ⋅ 1 = a, however ab ≠ 1
- Gröbner basis: ⟨a, b | a2b=a⟩
- Cancellative quotient is isomorphic to ℤ
- Enveloping group is isomorphic to ℤ
- 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:aab=a,baa=a ab - -
ba=ab
aab=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
14 total
| Σ | # | Presentation | Mapping |
|---|
| 8 | 648 | ⟨a, b | ba=ab, aab=a⟩ | φ(a) = a, φ(b) = b |
| 8 | 650 | ⟨a, b | ba=ab, aba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 4142 | ⟨a, b | aba=aab, baa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6352 | ⟨a, b | aab=a, baaab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6354 | ⟨a, b | aab=a, baaba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6358 | ⟨a, b | aab=a, babaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6474 | ⟨a, b | aba=a, baaab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6612 | ⟨a, b | aab=a, aabb=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 6620 | ⟨a, b | aab=a, abab=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 6630 | ⟨a, b | aab=a, baaa=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 6635 | ⟨a, b | aab=a, baab=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 6639 | ⟨a, b | aab=a, baba=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 6743 | ⟨a, b | aba=a, abab=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 6811 | ⟨a, b | aab=a, baa=aab⟩ | φ(a) = a, φ(b) = b |