#21051 ⟨a, b | ba=ab, aaaa=abb⟩
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- 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 ⋅ a3 = a4b and ab ⋅ b2 = a4b, however a3 ≠ b2
- Commutative Gröbner basis: ⟨a, b | ab2=a4⟩
- 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,aaaa=abb ab
ba=ab
aaaa=abb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 21052 | ⟨a, b | ba=ab, aaaa=bab⟩ | φ(a) = a, φ(b) = b |