User:Dfeuer/Definition:Normal Submagma

Definition
Let $(S,\circ)$ be a magma.

Let $(N,\circ)$ be a submagma.

Then $(N,\circ)$ is a normal submagma iff

Option 1
for each $x\in S$, $x\circ N = N \circ x$

Option 2
For each $a,b \in S$, $a \circ b \in N \implies b \circ a \in N$

I don't know if either implies the other, but I doubt it.