#7188 ⟨
a
,
b
|
ba
=
ab
,
aba
=
aab
⟩
Up:
Monoids with two generators and two relations
Prev:
#7186
⟨
a
,
b
|
ba
=
ab
,
aab
=
aaa
⟩
Next:
#7189
⟨
a
,
b
|
ba
=
ab
,
abb
=
aaa
⟩
Properties
Presentation has sum-of-sides 10
Isomorphic to ℕ ⊕ ℕ
Infinite cancellative commutative monoid
Commutative Gröbner basis: ⟨
a
,
b
| ⟩
Grothendieck group is isomorphic to ℤ ⊕ ℤ
Group of units is isomorphic to ℤ
1
4 Archimedian components:
1,
a
,
b
,
ab
Complete rewriting system
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
Reduction order:
Left-to-right shortlex with
a
<
b
ba
⇒
ab
# ab:ba=ab,aba=aab ab ba=ab
Staircase diagram
Right Cayley graph (truncated)
Other isomorphic instances
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
Σ
#
Presentation
Mapping
10
7192
⟨
a
,
b
|
ba
=
ab
,
baa
=
aab
⟩
φ
(
a
) =
a
,
φ
(
b
) =
b
