Iste articulo es in disveloppamento
Un o plus
wikipedistas labora al momento pro meliorar iste articulo. Per iste ration, le information del articulo poterea esser incomplete. Per favor, propone nove cambios in le
pagina de discussion .
Isto es un tabella de leges algebric nominate etiam axiomas . Le condition general de iste tabella es isto: Sia
(
M
;
∗
)
{\displaystyle (M;\ast )}
magma .
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
=
(
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
---
