Tabella de leges algebric

Isto es un tabella de leges algebric nominate alsi axiomas. Le condition general de iste tabella es isto: Sia $(M;\ast )$ un magma. Le classification eveni secundo le numeros del variabiles.

Nota

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Leges con un variabile

Lege	Nomine	Application in structuras
$\forall a\in M\;\;a\ast a=a$	idempotentia	---
$\forall a\in M\;\;(a\ast a)\ast a=a\ast (a\ast a)$	idemassociativitate	---

Leges con duo variabiles

Lege	Nomine	Application in structuras
$\forall b\in M\;\;a\ast b=a$	$a$ es un elemento L-absorbente	---
$\forall b\in M\;\;b\ast a=a$	$a$ es un elemento R-absorbente	---
$\forall b\in M\;\;a\ast b=b$	$a$ es un elemento L-neutre	loop, monoide, gruppo
$\forall b\in M\;\;b\ast a=b$	$a$ es un elemento R-neutre	loop, monoide, gruppo
$\forall a,b\in M\;\;a\ast b=b\ast a$	commutativitate	---
$\forall a,b\in M\;\;a\ast a=b\ast b$	unipotentia	---
$\forall a,b\in M\;\;a\ast (b\ast a)=b$	semisymmetria a sinsitra	---
$\forall a,b\in M\;\;(a\ast b)\ast a=b$	semisymmetria a dextra	---
$\forall a,b\in M\;\;a\ast (b\ast a)=b=(a\ast b)\ast a$	semisymmetria	---
$\forall a,b\in M\;\;a\ast (b\ast a)=(a\ast b)\ast a$	flexibilitate	---

Leges con tres variabiles

Lege	Nomine	Application in structuras
$\forall a,b,c\in M\;\;a\ast (b\ast c)=(a\ast b)\ast c$	associativitate	semigruppo, gruppo, anello, algebra associative, corpore

Leges con quatro variabiles

Lege	Nomine	Application in structuras
$\forall a,b,c,d\in M\;\;(a\ast b)\ast (c\ast d)=(a\ast c)\ast (b\ast d)$	medialitate	---

Litteratura

Ilse, D., Lehmann, I., Schulz, W.: Gruppoide und Funktionalgleichungen, VEB Deutscher Verlag der Wissenschaften, Berlin 1984, p. 67 – 68