Template:Ring theory sidebar

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| title = Algebraic structure → Ring theory
Ring theory

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| list2name = Basic

| list2title = Basic concepts

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| list2 =

Rings

: • Subrings

: • Ideal

: • Quotient ring

:: • Fractional ideal

:: • Total ring of fractions

: • Product of rings

: • Free product of associative algebras

: • Tensor product of algebras

Ring homomorphisms

: • Kernel

: • Inner automorphism

: • Frobenius endomorphism

Algebraic structures

: • Module

: • Associative algebra

: • Graded ring

: • Involutive ring

: • Category of rings

:: • Initial ring $\mathbb{Z}$

:: • Terminal ring $0 = \mathbb{Z}/1\mathbb{Z}$

Related structures

: • Field

:: • Finite field

: • Non-associative ring

:: • Lie ring

:: • Jordan ring

:: • Semifield

| list3name = Commutative

| list3title = Commutative algebra

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Commutative rings

: • Integral domain

:: • Integrally closed domain

:: • GCD domain

:: • Unique factorization domain

:: • Principal ideal domain

:: • Euclidean domain

:: • Field

::: • Finite field

:: • Polynomial ring

:: • Formal power series ring

Algebraic number theory

: • Algebraic number field

: • Integers modulo n

: • Ring of integers

: • p-adic integers $\mathbb{Z}_p$

: • p-adic numbers $\mathbb{Q}_p$

: • Prüfer p-ring $\mathbb{Z}(p^\infty)$

| list4name = Noncommutative

| list4title = Noncommutative algebra

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Noncommutative rings

: • Division ring

: • Semiprimitive ring

: • Simple ring

: • Commutator

Noncommutative algebraic geometry

Free algebra

Clifford algebra

: • Geometric algebra

Operator algebra

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