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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Fields
A field is a commutative ring where every nonzero element has a multiplicative inverse.
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Field extensions
A field extension contains a smaller field and can be viewed as its vector space.
Finite fields
A finite field has prime-power size; fields of each such size exist and are unique up to isomorphism.
Ideals
An ideal is an additive subgroup closed under multiplication by ring elements on the required sides.
Polynomial rings
Polynomials over a ring form a ring with coefficientwise addition and polynomial multiplication.
Prime factorization
Every integer greater than one factors uniquely into primes up to their order.
Knowledge connections
- Ideals · Related · Map context
- Polynomial rings · Related · Map context
- Field extensions · Next concept · Map context
- Prime factorization · Related · Map context
- Prime number theorem · Related · Map context
- Finite fields · Next concept · Map context
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Number Theory
Explore divisibility and congruences; arithmetic functions and equations; prime distribution and advanced connections. Concepts and connections are available independently of video coverage.