Monoid Ideal
A subset
I
⊆
M
𝐼
𝑀
I\subseteq M
of a
Monoid
M
𝑀
M
is a
Left ideal
if for all
x
i
:
X
:
𝑥
𝑖
𝑋
xi:X
,
i
∈
I
⇒
x
i
∈
I
𝑖
𝐼
⇒
𝑥
𝑖
𝐼
i\in I\Rightarrow xi\in I
Right ideal
if for all
i
x
:
X
:
𝑖
𝑥
𝑋
ix:X
,
i
∈
I
⇒
i
x
∈
I
𝑖
𝐼
⇒
𝑖
𝑥
𝐼
i\in I\Rightarrow ix\in I
Two-sided ideal
if it is both a left and right ideal.
Properties
Backlinks
Principal Ideal in a Monoid
Monoid Congruence
Rees Congruence