1 | A module is an Abelian group over a ring as contrasted with a vector space which is an Abelian group over a field. The scalars form a ring and just like in a vector space, scalar multiplication is defined. However, in a ring the multiplicative inverses do not exist in general for the elements, which makes all the difference! |

http://www.livingreviews.org/lrr-2005-4 |
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