module (Q18848)
generalization of vector space, with scalars in a ring instead of a field
Language:
Current Data About module
(P279) (Q181296)

(P461) (Q5155179)

(P527) (Q181296)

(Q161172)
(P3831)

(P1889) (Q120812)
(P143)
(P4656) https://pl.wikipedia.org/w/index.php?title=Moduł_(matematyka)&oldid=64327401

(P2534) \begin{aligned}m+n&=n+m &&(m,n\in M)\\ (m+n)+p&=m+(n+p)&&(m,n,p\in M) \\ m+0_M &= m&&(m\in M) \\ (-m)+m &= 0_M&&(m\in M) \\ r(sm) &= (rs)m &&(m\in M,\;r,s\in R)\\ 1_Rm &=m&&(m\in M) \\ r(m+n)&=rm+rn&&(m,n\in M,\;r\in R) \\ (r+s)m &= rm+sm&&(m\in M,\;r,s\in R)\end{aligned}

(P2579) (Q727659)

(Q114722746)

(P5008) (Q6173448)
(P585) Monday, October 31, 2022

(P6104) (Q8487137)

(P7235) m+n=n+m\qquad(m,n\in M)
(P9758)

\begin{aligned}(m+n)+p&=m+(n+p)&&(m,n,p\in M) \\r(sm) &= (rs)m &&(m\in M,\;r,s\in R)\\\end{aligned}
(P9758)

0_M
(P9758)

-m
(P9758)

1_R
(P9758)
(P642)

\begin{aligned}r(m+n)&=rm+rn&&(m,n\in M,\;r\in R) \\(r+s)m &= rm+sm&&(m\in M,\;r,s\in R)\end{aligned}
(P9758)