List of abstract-algebra notes:

• Principal ideal domain
• Construction of p-adic numbers
• Dedekind ring
• Hensel's Lemma
• Integral closure
• Noetherian ring
• P-adic metric
• Discrete valuation ring
• Radical of an ideal
• Unique factorization domain
• Krull dimension
• Bezout domain
• Ideals of rings
• Projective limit
• Group action
• Splitting field
• Category of fields
• Characterizing finite fields
• Degree of a field extension
• Distinguished class of extensions
• Irreducible polynomial of an element
• Real closed field
• Algebraic closure of a field
• Extension field
• Field embedding
• Normal field extension
• Krasner's Lemma
• Separable extension
• Roots of unity in Qp
• Transcendence basis
• Extending the p-adic norm
• R-Module
• Integrally equivalent forms
• Congruent and equivalent polynomials
• DLOG cryptosystem
• Euler's Theorem
• Elliptic curve
• Quadratic residues modulo m
• Polynomials versus forms
• Types of primes
• Algebraic number field
• Lagrange's Theorem
• Quadratic Gauss sum
• Chevalley's Theorem
• Decomposable form
• Exact sequence
• Preorder
• Closure operator
• Galois connection
• Matrix groups and linear groups
• Power series in finite fields
• Product of lattices
• Distributive lattice
• Lattice
• Algebraic addition theorem