Abstract Algebra
Explore groups and symmetry; rings and fields; extensions and actions. Concepts and connections are available independently of video coverage.
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Rings
A ring supports addition and multiplication linked by distributive laws.
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Affine varieties
Common polynomial zero sets define affine algebraic sets over a chosen field.
Algebraic dimension
Chains of prime ideals define Krull dimension and connect algebraic structure to geometric dimension.
Binary operations
A binary operation combines two elements into one in a specified set.
Coordinate rings
Polynomial functions on an affine algebraic set form a quotient by its vanishing ideal.
Field extensions
A field extension contains a smaller field and can be viewed as its vector space.
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- Ideals · Related · Map context
- Modules · Related · Map context
- Binary operations · Related · Map context
- Field extensions · Related · Map context
- Ideals · Next concept · Map context
- Polynomials · Related · Map context
- Affine varieties · Related · Map context
- Algebraic dimension · Related · Map context
- Coordinate rings · Next concept · Map context
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Algebraic Geometry
Explore polynomial geometry; local algebra and schemes; geometric properties. Concepts and connections are available independently of video coverage.