A field is algebraically closed when every nonconstant polynomial over it has a root in it, equivalently when every such polynomial splits into linear factors.
Ancestors (5)
Incoming links (68)
- Algebraic cotangent space
- Algebraic quotient by a finite group
- Closed-point dimension lemma for affine domains
- Completion of an algebraic closure of a p-adic field is algebraically closed
- Coordinate ring of a product of affine varieties
- Failure of Lie theorem in positive characteristic
- Finite-dimensional division algebra over an algebraically closed field
- Hilbert Nullstellensatz
- Ideal sheaf of two closed points
- Jordan–Chevalley decomposition
- Lie-invariant bilinear form
- Nonfinite generation of elliptic-curve divisor class groups
- Past exam of the mathematics course of the University of Cambridge / 2001 / iii / Paper 14 / 1 / c / Solution
- Past exam of the mathematics course of the University of Cambridge / 2001 / iii / Paper 14 / 2 / b / Solution
- Past exam of the mathematics course of the University of Cambridge / 2001 / iii / Paper 14 / 3 / b / i / Solution
- Past exam of the mathematics course of the University of Cambridge / 2001 / iii / Paper 4 / 3 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2003 / iii / Paper 15 / 1 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2003 / iii / Paper 15 / 2 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 80 / 1 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 14 / 2 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 3 / 6 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 23 / 5 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 18 / 1 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 18 / 3 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 21 / 1 / a / Solution
- Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 21 / 1 / b / Solution
- Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 21 / 2 / c / Solution
- Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 21 / 5 / a / Solution
- Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 2 / 1 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 2 / 3 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 2 / 4 / ii / Solution
- Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 3 / 2 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2012 / iii / Paper 13 / 1 / i / Solution
- Past exam of the mathematics course of the University of Cambridge / 2012 / iii / Paper 13 / 4 / i / Solution
- Past exam of the mathematics course of the University of Cambridge / 2012 / iii / Paper 13 / 5 / ii / Solution
- Past exam of the mathematics course of the University of Cambridge / 2012 / iii / Paper 13 / 5 / i / Solution
- Past exam of the mathematics course of the University of Cambridge / 2012 / iii / Paper 21 / 1 / 2 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2012 / iii / Paper 21 / 1 / 4 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2012 / iii / Paper 4 / 3 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 1 / 1 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 2 / 2 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 2 / 1 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 3 / 4 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 2 / 1 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2016 / iii / Paper 101 / 2 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2016 / iii / Paper 102 / 1 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2016 / iii / Paper 102 / 3 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2017 / iii / Paper 102 / 2 / i / Solution
- Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 3 / 24I / b / Solution
- Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 2 / 24F / a / Solution
- Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 144 / 2 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 3 / 18H / b / Solution
- Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 3 / 18H / c / Solution
- Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 101 / 3 / a / Solution
- Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 3 / 24G / Solution
- Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 101 / 2 / iv / Solution
- Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 101 / 4 / i / Solution
- Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 101 / 3 / i / Solution
- Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 144 / 4 / c / Solution
- Picard group of a smooth affine quadric surface
- Prevariety
- Projective Nullstellensatz
- Segre description of a smooth quadric surface
- Semisimple quotient of a module endomorphism algebra
- Smooth quadric surface
- Tsen theorem
- Two-dimensional subalgebra criterion for Lie algebra nilpotence
- Unipotent matrix
Discussion (0)
New discussionThere are no discussions about this article yet.
Articles by others on the same topic (1)
An **algebraically closed field** is a field \( F \) in which every non-constant polynomial equation with coefficients in \( F \) has at least one root in \( F \).