#7122 ⟨a, b | ba=ab, aaab=ab⟩

Properties

Presentation has sum-of-sides 10
Infinite non-cancellative commutative monoid
Commutative Gröbner basis: ⟨a, b | a³b=ab⟩
Not cancellative, because multiplication by ab is not injective:
- a² ≠ 1
- ab ⋅ a² = ab
- ab ⋅ 1 = ab
- Cancellative quotient is isomorphic to ℤ₂ ⊕ ℕ
Grothendieck group is isomorphic to ℤ₂ ⊕ 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,aaab=ab ab
ba=ab
aaab=ab

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

3 total

Σ	#	Presentation	Mapping
10	7123	⟨a, b \| ba=ab, aaab=ba⟩	φ(a) = a, φ(b) = b
10	7126	⟨a, b \| ba=ab, aaba=ab⟩	φ(a) = a, φ(b) = b
10	7127	⟨a, b \| ba=ab, aaba=ba⟩	φ(a) = a, φ(b) = b

Up:	Monoids with two generators and two relations
Prev:	#7121 ⟨a, b \| ba=ab, aaab=aa⟩
Next:	#7124 ⟨a, b \| ba=ab, aaab=bb⟩