#20852 ⟨a, b | ba=ab, aaaab=ab⟩

Properties

Presentation has sum-of-sides 11
Infinite non-cancellative commutative monoid
Commutative Gröbner basis: ⟨a, b | a⁴b=ab⟩
Not cancellative, because multiplication by ab is not injective:
- a³ ≠ 1
- ab ⋅ a³ = ab
- ab ⋅ 1 = ab
- Cancellative quotient is isomorphic to ℤ₃ ⊕ ℕ
Grothendieck group is isomorphic to ℤ₃ ⊕ ℤ
Group of units is isomorphic to ℤ₁
4 Archimedian components:
- 1, a, b, ab

Format:	Pretty Plain
Word to reduce:
	Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Reduction strategy:	Leftmost Rightmost
Path to normal form:	1 1

# ab:ba=ab,aaaab=ab ab
ba=ab
aaaab=ab

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

4 total

Σ	#	Presentation	Mapping
11	20853	⟨a, b \| ba=ab, aaaab=ba⟩	φ(a) = a, φ(b) = b
11	20856	⟨a, b \| ba=ab, aaaba=ab⟩	φ(a) = a, φ(b) = b
11	20857	⟨a, b \| ba=ab, aaaba=ba⟩	φ(a) = a, φ(b) = b
11	20864	⟨a, b \| ba=ab, aabaa=ab⟩	φ(a) = a, φ(b) = b

Up:	Monoids with two generators and two relations
Prev:	#20851 ⟨a, b \| ba=ab, aaaab=aa⟩
Next:	#20854 ⟨a, b \| ba=ab, aaaab=bb⟩