Induced magma power set magma

Set

context $\langle\!\langle M,* \rangle\!\rangle$ … magma
definiendum $\langle\!\langle {\mathcal P}M,\star \rangle\!\rangle$
definition $\star\in$ binary operation on ${\mathcal P}M$
definition $S\star T:=\{x*y\ |\ x\in S, y\in T\}$

Discussion

When talking about left cosets etc., people write $xS$ for $\{x\}S$.

Reference

Wikipedia: Magma


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