#3440 ⟨a, b, c | ba=ac, aac=a⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 8
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ ad = a and a ⋅ 1 = a, however ad ≠ 1
- Not right cancellative, because right multiplication by d is not injective:
-
da ⋅ d = d and 1 ⋅ d = d, however da ≠ 1
- Auxiliary generators:
- d = cac
- Reduction order:
- Left-to-right shortlex with a < b < d < c
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# abc:ba=ac,aac=a abdc cac=d morph:3/1
ac=ad
ba=ad
dc=dd
aad=a
dad=d
cad=d
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 8 | 3443 | ⟨a, b, c | ba=ac, aba=a⟩ | φ(a) = a, φ(b) = b, φ(c) = c |