Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
General Math
Calculus
Differential Equations
Topology and Analysis
Linear and Abstract Algebra
Differential Geometry
Set Theory, Logic, Probability, Statistics
MATLAB, Maple, Mathematica, LaTeX
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
General Math
Calculus
Differential Equations
Topology and Analysis
Linear and Abstract Algebra
Differential Geometry
Set Theory, Logic, Probability, Statistics
MATLAB, Maple, Mathematica, LaTeX
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Mathematics
Linear and Abstract Algebra
Commutative algebra and differential geometry
Reply to thread
Message
[QUOTE="mathwonk, post: 6487128, member: 13785"] in other words, given a maximal ideal, look at all points where all functions in that ideal vanish. if the base field is algebraically closed, there will be exactly one such point. hence a maximal ideal recovers a point of the variety. if the base field is not algebraically closed, there will be more maximal ideals than points. e.g. over the real numbers R, if m is a maximal ideal of R[X], then R[X]/M will be isomorophic either to R or to C, the complex numbers. The ones corresponding to single points of R are the ones where the quotient field is R, and those maximal ideals where the quotient field is isomorphic to C, correspond to pairs of conjugate complex points. I.e. maximal ideals of R[X] are generated by irreducible polynomials over R, and these are either linear (corresponding to a single real point), or quadratic (corresponding to a pair of conjugate complex points). [/QUOTE]
Insert quotes…
Post reply
Forums
Mathematics
Linear and Abstract Algebra
Commutative algebra and differential geometry
Back
Top