Modules & Ideals: A Closer Look

[fk378]

General question:

Is there some relationship between vector spaces/modules and ideal of a ring? In both vector spaces/modules and ideals, we have closure under addition and also it "swallows" elements from the field and ring, respectively.

 

[quantumdude]

Hmmm...The only answer I can think of off the top of my head is that every ideal of a ring R is also a submodule of R. That's not too profound though, as every ring R is a module over itself.