Submagma (mathematica)

In mathematica, ${\boldsymbol {N}}$ es un submagma de ${\boldsymbol {M}}$ $:\Leftrightarrow$ ${\boldsymbol {N}}\leq {\boldsymbol {M}}$ $:\Leftrightarrow$ ${\boldsymbol {M}}$ es un magma $\wedge$ ${\boldsymbol {N}}$ es un magma $\wedge$ $\exists M,N,\ast ,\diamond$ con $((M;\ast )={\boldsymbol {M}}\;\wedge \;(N;\diamond )={\boldsymbol {N}})$ tal que $(N\subseteq M\;\wedge \;\forall a,b\in N\;a\diamond b=a\ast b)$

In iste caso, ${\boldsymbol {M}}$ es un supermagma de ${\boldsymbol {N}}$: ${\boldsymbol {M}}\geq {\boldsymbol {N}}$.

Submagma proprie

${\boldsymbol {N}}$ es un submagma proprie de ${\boldsymbol {M}}$ $:\Leftrightarrow$ ${\boldsymbol {N}}<{\boldsymbol {M}}$ $:\Leftrightarrow$ ${\boldsymbol {N}}\leq {\boldsymbol {M}}\;\wedge \;{\boldsymbol {N}}\neq {\boldsymbol {M}}$.

Submagma trivial

Sia ${\boldsymbol {M}}$ un magma. ${\boldsymbol {N}}$ es un submagma trivial de ${\boldsymbol {M}}$ $:\Leftrightarrow$ (${\boldsymbol {N}}$ es le magma vacue) $\vee$ ${\boldsymbol {N}}={\boldsymbol {M}}$.