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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