#2263 ⟨a, b | ba=ab, aab=aa⟩
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- Properties
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Presentation has sum-of-sides 9
- Infinite non-cancellative commutative monoid
- Not cancellative, because multiplication by a2 is not injective:
-
a2 ⋅ b = a2 and a2 ⋅ 1 = a2, however b ≠ 1
- Commutative Gröbner basis: ⟨a, b | a2b=a2⟩
- Cancellative quotient is isomorphic to ℕ
- 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,aab=aa ab
ba=ab
aab=aa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 9 | 2267 | ⟨a, b | ba=ab, aba=aa⟩ | φ(a) = a, φ(b) = b |