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{{in uso | data = 2026-03-07}} Isto es un tabella de leges algebric nominate alsi axiomas . Le condition general de iste tabella es isto: Sia
(
M
;
∗
)
{\displaystyle (M;\ast )}
magma . Le classification eveni secundo le numeros del variabiles .
Lege
Nomine
Application in structuras
∀
a
∈
M
a
∗
a
=
a
{\displaystyle \forall a\in M\;\;a\ast a=a}
idempotentia ---
∀
a
∈
M
(
a
∗
a
)
∗
a
=
a
∗
(
a
∗
a
)
{\displaystyle \forall a\in M\;\;(a\ast a)\ast a=a\ast (a\ast a)}
idemassociativitate ---
Lege
Nomine
Application in structuras
∀
b
∈
M
a
∗
b
=
a
{\displaystyle \forall b\in M\;\;a\ast b=a}
a
{\displaystyle a}
---
∀
b
∈
M
b
∗
a
=
a
{\displaystyle \forall b\in M\;\;b\ast a=a}
a
{\displaystyle a}
---
∀
b
∈
M
a
∗
b
=
b
{\displaystyle \forall b\in M\;\;a\ast b=b}
a
{\displaystyle a}
elemento L-neutre loop , monoide , gruppo
∀
b
∈
M
b
∗
a
=
b
{\displaystyle \forall b\in M\;\;b\ast a=b}
a
{\displaystyle a}
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 ---
∀
a
,
b
∈
M
a
∗
a
=
b
∗
b
{\displaystyle \forall a,b\in M\;\;a\ast a=b\ast b}
unipotentia ---
∀
a
,
b
∈
M
a
∗
(
b
∗
a
)
=
b
{\displaystyle \forall a,b\in M\;\;a\ast (b\ast a)=b}
semisymmetria a sinsitra ---
∀
a
,
b
∈
M
(
a
∗
b
)
∗
a
=
b
{\displaystyle \forall a,b\in M\;\;(a\ast b)\ast a=b}
semisymmetria a dextra ---
∀
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 ---
∀
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 ---
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 ---
Ilse, D., Lehmann, I., Schulz, W.: Gruppoide und Funktionalgleichungen , VEB Deutscher Verlag der Wissenschaften, Berlin 1984, p. 67 – 68
