You are here
Home ›exact sequence
Primary tabs
exact sequence
If we have two homomorphisms and in some category of modules, then we say that and are exact at if the image of is equal to the kernel of .
A sequence of homomorphisms
is said to be exact if each pair of adjacent homomorphisms is exact – in other words if for all .
Compare this to the notion of a chain complex.
Remark. The notion of exact sequences can be generalized to any abelian category , where and above are objects and morphisms in .
Type of Math Object:
Definition
Major Section:
Reference
Mathematics Subject Classification
16-00 General reference works (handbooks, dictionaries, bibliographies, etc.)- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)
- Other useful stuff
Recent Activity
May 17
new image: sinx_approx.png by jeremyboden
new image: approximation_to_sinx by jeremyboden
new image: approximation_to_sinx by jeremyboden
new question: Solving the word problem for isomorphic groups by mairiwalker
new image: LineDiagrams.jpg by m759
new image: ProjPoints.jpg by m759
new image: AbstrExample3.jpg by m759
new image: four-diamond_figure.jpg by m759
May 16
new problem: Curve fitting using the Exchange Algorithm. by jeremyboden
new question: Undirected graphs and their Chromatic Number by Serchinnho
new image: sinx_approx.png by jeremyboden
new image: approximation_to_sinx by jeremyboden
new image: approximation_to_sinx by jeremyboden
new question: Solving the word problem for isomorphic groups by mairiwalker
new image: LineDiagrams.jpg by m759
new image: ProjPoints.jpg by m759
new image: AbstrExample3.jpg by m759
new image: four-diamond_figure.jpg by m759
May 16
new problem: Curve fitting using the Exchange Algorithm. by jeremyboden
new question: Undirected graphs and their Chromatic Number by Serchinnho


