Generating set for finitely generated submodule of finitely generated module
Let $R$ be a ring, $M$ a finitely generated $R$-module, and $N \subseteq M$ a f.g. submodule. Suppose $M$ has a minimal generating set of $m$ elements, then under what conditions may we assume that $N$ has a (not necessarily minimal) generating set of $n \leq m$ generators? I know the result holds, for example, when $R$ is a PID, but are there any other sufficient (or even necessary) conditions on $R$ (and/or $M,N$) to provide a complete characterization? A reference would be welcome.
Elviegem
41
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
1 Attachment
Erdos
4.8K
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 400 views
- $20.00
Related Questions
- Need to figure distance between two points/lines.
- How do you prove that when you expand a binomial like $(a+b)^n$ the coefficients can be calculated by going to the n row in Pascal's triangle?
- Fields and Galois theory
- Graph Equation from Test
- Motorcycle Valve Clearance Calculation and Spacer Size Word Problem
- Algebra Word Problem 3
- Algebra 1 Word Problem #3
- Algebra problem
