jaj•a•person's notes

Paolo Aluffi

Algebra: Chapter 0

978-0-8218-4781-7

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Adjoining a root to a field
Algebraic closure
Bound on the automorphism group of a finite simple extension
Canonical decomposition
Cayley's theorem for rings
Compositions only of algebraic extensions are algebraic
Eisenstein's criterion
Finite extension of a Galois field
GCD
Galois extension
Galois field
Maximal ideal iff prime ideal in a PID
Module-finite R-monoid
Noetherian module
Normal extension
Perfect field
Polynomial ring over a UFD is a UFD
Polynomial ring
Principal ideal domain
Ring
Separability of a finite extension
Separable polynomial
Simple extension
Splitting field
Tensor product of modules over a commutative ring
Unique factorization domain
Unit
Zero ring
Zero-divisor

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