nLab algebra - contents

• algebra, higher algebra
• universal algebra
• monoid, semigroup, quasigroup
• nonassociative algebra
• associative unital algebra
• commutative algebra
• Lie algebra, Jordan algebra
• Leibniz algebra, pre-Lie algebra
• Poisson algebra, Frobenius algebra
• lattice, frame, quantale
• Boolean ring, Heyting algebra
• commutator, center
• monad, comonad
• distributive law

Group theory

• group, normal subgroup
• action, Cayley's theorem
• centralizer, normalizer
• abelian group, cyclic group
• group extension, Galois extension
• algebraic group, formal group
• Lie group, quantum group

Ring theory

• ring, commutative ring

• local ring, Artinian ring

• Noetherian ring

• skewfield, field

• integral domain

• ideal, prime ideal, maximal ideal

• Ore localization

• group extension

• central simple algebra

• derivation, Ore extension

Module theory

• module, bimodule

• vector space, linear algebra

• matrix, eigenvalue, trace

• determinant, quasideterminant

• representation theory, Schur lemma

• extension of scalars

• restriction of scalars

• Frobenius reciprocity

• Morita equivalence, Morita context

• Wedderburn-Artin theorem

• abelian category, additive category

• monoidal category, Tannaka duality

Gebras

• coalgebra, coring

• bialgebra, Hopf algebra

• comodule, Hopf module

• Yetter-Drinfeld module

• associative bialgebroid

• dual gebra, cotensor product

• Hopf-Galois extension