0
votes
0answers
102 views

When does the rank of a module behave sub-multiplicatively under tensoring?

Let $\cal{E}$ be a finitely generated projective bimodule over a (noncommutative) algebra $A$. Moreover, let us assume that $\cal{E}$ is of finite rank $n$. The tensor product $ \cal{E} \otimes_A ...
8
votes
1answer
4k views

Rank of a module

What's wrong with defining the rank of a finitely generated module over any (commutative) ring to be just the smallest number of generators? All books I know define rank only locally this way. But why ...
4
votes
1answer
2k views

Dimension of module

Does dimension of a module (say, dimension of its support) have anything to do with the supremum length of chains of prime submodules like rings? Let's restrict to finitely generated modules over ...