User:KBlott/Definition/Commutative Class Monoid
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Definition
Let $(C,*)$ be a class monoid.
Then,
- $(C,*)$ is called a commutative class monoid (or CC monoid)
iff
- $\forall x,y \in C, x*y = y*x$
iff
- $\forall x,y \in C,\left[ =(*(x,y),*(y,x))\right]$
iff
- $\left[ x,y \in C \right] \implies \left[ =(*(x,y),*(y,x))\right]$
iff
- $\left[ (x \in C)\wedge (y \in C) \right] \implies \left[ =(*(x,y),*(y,x))\right]$
iff
- $\left[ (x \in C)\wedge (y \in C) \right] \implies \left[ (* (x,y)\subset *(y,x))\wedge (y,x)\subset *(x,y)) \right]$