#20655 ⟨a, b | ba=ab, aaaabb=b⟩
Quick links
- Properties
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Presentation has sum-of-sides 11
- Infinite non-cancellative commutative monoid
- Not cancellative, because multiplication by ab is not injective:
-
ab ⋅ a4b = ab and ab ⋅ 1 = ab, however a4b ≠ 1
- Commutative Gröbner basis: ⟨a, b | a4b2=b⟩
- 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:ba=ab,aaaabb=b ab
ba=ab
aaaabb=b
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
8 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 20659 | ⟨a, b | ba=ab, aaabab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 20661 | ⟨a, b | ba=ab, aaabba=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 20664 | ⟨a, b | ba=ab, aabaab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 20666 | ⟨a, b | ba=ab, aababa=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 20669 | ⟨a, b | ba=ab, aabbaa=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 20675 | ⟨a, b | ba=ab, abaaab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 20677 | ⟨a, b | ba=ab, abaaba=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 20682 | ⟨a, b | ba=ab, abbbba=a⟩ | φ(a) = b, φ(b) = a |