Isto es un tabella de leges algebric nominate alsi axiomas . Le condition general de iste tabella es isto: Sia ( M ; ∗ ) {\displaystyle (M;\ast )} un magma . Le classification eveni secundo le numeros del variabiles .
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Leges con un variabile
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Lege
Nomine
Application in structuras
∀ a ∈ M a ∗ a = a {\displaystyle \forall a\in M\;\;a\ast a=a}
idempotentia
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∀ a ∈ M ( a ∗ a ) ∗ a = a ∗ ( a ∗ a ) {\displaystyle \forall a\in M\;\;(a\ast a)\ast a=a\ast (a\ast a)}
idemassociativitate
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Leges con duo variabiles
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Lege
Nomine
Application in structuras
∀ b ∈ M a ∗ b = a {\displaystyle \forall b\in M\;\;a\ast b=a}
a {\displaystyle a} es un elemento L-absorbente
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∀ b ∈ M b ∗ a = a {\displaystyle \forall b\in M\;\;b\ast a=a}
a {\displaystyle a} es un elemento R-absorbente
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∀ b ∈ M a ∗ b = b {\displaystyle \forall b\in M\;\;a\ast b=b}
a {\displaystyle a} es un elemento L-neutre
loop , monoide , gruppo
∀ b ∈ M b ∗ a = b {\displaystyle \forall b\in M\;\;b\ast a=b}
a {\displaystyle a} es un elemento R-neutre
loop , monoide , gruppo
∀ a , b ∈ M a ∗ b = b ∗ a {\displaystyle \forall a,b\in M\;\;a\ast b=b\ast a}
commutativitate
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∀ a , b ∈ M a ∗ a = b ∗ b {\displaystyle \forall a,b\in M\;\;a\ast a=b\ast b}
unipotentia
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∀ a , b ∈ M a ∗ ( b ∗ a ) = b {\displaystyle \forall a,b\in M\;\;a\ast (b\ast a)=b}
semisymmetria a sinsitra
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∀ a , b ∈ M ( a ∗ b ) ∗ a = b {\displaystyle \forall a,b\in M\;\;(a\ast b)\ast a=b}
semisymmetria a dextra
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∀ a , b ∈ M a ∗ ( b ∗ a ) = b = ( a ∗ b ) ∗ a {\displaystyle \forall a,b\in M\;\;a\ast (b\ast a)=b=(a\ast b)\ast a}
semisymmetria
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∀ a , b ∈ M a ∗ ( b ∗ a ) = ( a ∗ b ) ∗ a {\displaystyle \forall a,b\in M\;\;a\ast (b\ast a)=(a\ast b)\ast a}
flexibilitate
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Leges con tres variabiles
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Leges con quatro variabiles
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Lege
Nomine
Application in structuras
∀ a , b , c , d ∈ M ( a ∗ b ) ∗ ( c ∗ d ) = ( a ∗ c ) ∗ ( b ∗ d ) {\displaystyle \forall a,b,c,d\in M\;\;(a\ast b)\ast (c\ast d)=(a\ast c)\ast (b\ast d)}
medialitate
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Ilse, D., Lehmann, I., Schulz, W.: Gruppoide und Funktionalgleichungen , VEB Deutscher Verlag der Wissenschaften, Berlin 1984, p. 67 – 68