#5399 ⟨a, b | aab=ba, bab=ab⟩
Contents
- Properties
- Commutative structure
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative commutative monoid
- Element a has infinite order
- Not cancellative, because multiplication by ab is not injective:
-
ab ⋅ b = ab and ab ⋅ 1 = ab, however b ≠ 1
- Gröbner basis: ⟨a, b | ab2=ab, a2b=ab⟩
- Cancellative quotient is isomorphic to ℤ1
- Enveloping group is isomorphic to ℤ1
- Group of units is isomorphic to ℤ1
- 4 Archimedian components:
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aab=ba,bab=ab ab - -
ba=ab
aab=ab
abb=ab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
7 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 5403 | ⟨a, b | aab=ba, bba=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 16222 | ⟨a, b | aab=ba, aabb=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 16246 | ⟨a, b | aab=ba, baab=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 16250 | ⟨a, b | aab=ba, baba=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 16258 | ⟨a, b | aab=ba, bbaa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 16395 | ⟨a, b | aba=ab, abab=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 16399 | ⟨a, b | aba=ab, abba=ba⟩ | φ(a) = a, φ(b) = b |