In mathematica, N {\displaystyle {\boldsymbol {N}}} es un submagma de M {\displaystyle {\boldsymbol {M}}} :⇔ ⇔ --> {\displaystyle :\Leftrightarrow } N ≤ ≤ --> M {\displaystyle {\boldsymbol {N}}\leq {\boldsymbol {M}}} :⇔ ⇔ --> {\displaystyle :\Leftrightarrow } M {\displaystyle {\boldsymbol {M}}} es un magma ∧ ∧ --> {\displaystyle \wedge } N {\displaystyle {\boldsymbol {N}}} es un magma ∧ ∧ --> {\displaystyle \wedge } ∃ ∃ --> M , N , ∗ ∗ --> , ⋄ ⋄ --> {\displaystyle \exists M,N,\ast ,\diamond } con ( ( M ; ∗ ∗ --> ) = M ∧ ∧ --> ( N ; ⋄ ⋄ --> ) = N ) {\displaystyle ((M;\ast )={\boldsymbol {M}}\;\wedge \;(N;\diamond )={\boldsymbol {N}})} tal que ( N ⊆ ⊆ --> M ∧ ∧ --> ∀ ∀ --> a , b ∈ ∈ --> N a ⋄ ⋄ --> b = a ∗ ∗ --> b ) {\displaystyle (N\subseteq M\;\wedge \;\forall a,b\in N\;a\diamond b=a\ast b)}
In iste caso, M {\displaystyle {\boldsymbol {M}}} es un supermagma de N {\displaystyle {\boldsymbol {N}}} : M ≥ ≥ --> N {\displaystyle {\boldsymbol {M}}\geq {\boldsymbol {N}}} .
N {\displaystyle {\boldsymbol {N}}} es un submagma proprie de M {\displaystyle {\boldsymbol {M}}} :⇔ ⇔ --> {\displaystyle :\Leftrightarrow } N < M {\displaystyle {\boldsymbol {N}}<{\boldsymbol {M}}} :⇔ ⇔ --> {\displaystyle :\Leftrightarrow } N ≤ ≤ --> M ∧ ∧ --> N ≠ ≠ --> M {\displaystyle {\boldsymbol {N}}\leq {\boldsymbol {M}}\;\wedge \;{\boldsymbol {N}}\neq {\boldsymbol {M}}} .
Sia M {\displaystyle {\boldsymbol {M}}} un magma. N {\displaystyle {\boldsymbol {N}}} es un submagma trivial de M {\displaystyle {\boldsymbol {M}}} :⇔ ⇔ --> {\displaystyle :\Leftrightarrow } ( N {\displaystyle {\boldsymbol {N}}} es le magma vacue) ∨ ∨ --> {\displaystyle \vee } N = M {\displaystyle {\boldsymbol {N}}={\boldsymbol {M}}} .
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