子模

设M是左R-模和N是M的子群,则N是一个R中左子模（或更明确叫左R-子模），即如果R中任何r，N中任何n，rn还在N中。相应的如果R中任何r，N中任何n，nr还在N中，叫右R-子模。

一个给定的模M的子模N1，N2，N3，两个二元运算，+，∩，满足格的模律，且子模N1是N2子集，则： (N1 + N3) ∩ N2 = N1 + (N3 ∩ N2).

参考

F.W. Anderson and K.R. Fuller: Rings and Categories of Modules, Graduate Texts in Mathematics, Vol. 13, 2nd Ed., Springer-Verlag, New York, 1992, ISBN 0-387-97845-3, ISBN 3-540-97845-3
Nathan Jacobson. Structure of rings. Colloquium publications, Vol. 37, 2nd Ed., AMS Bookstore, 1964, ISBN 978-0-8218-1037-8
Why is it a good idea to study the modules of a ring ? on MathOverflow.

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