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<includeonly>((sidebar with collapsible lists
| name = Ring theory sidebar
| class = plainlist
| style = width: 20.5em;
| titlestyle = padding-bottom:0.4em;
| title = <span style="font-size: 8pt; font-weight: none">[[Algebraic structure]] → Ring theory</span><br />[[Ring theory]]
| caption = 
| listtitlestyle = text-align:center;
| expanded = (({expanded|(({1|none))))))

| list2name = Basic
| list2title = Basic concepts
| list2style = text-align: left;
| list2 =
'''[[Ring (mathematics)|Ring]]s'''
:• [[Subring]]s
:• [[Ideal (ring theory)|Ideal]]
:• [[Quotient ring]]
::• [[Fractional ideal]]
::• [[Total ring of fractions]]
:• [[Product of rings]]
:•&nbsp;[[Free product of associative algebras]]
:• [[Tensor product of algebras]]

'''[[Ring homomorphism]]s'''
:• [[Kernel (algebra)#Ring_homomorphisms|Kernel]]
:• [[Inner_automorphism#Ring_case|Inner automorphism]]
:• [[Frobenius endomorphism]]

'''[[Algebraic structure]]s'''
:• [[Module (mathematics)|Module]]
:• [[Associative algebra]]
:• [[Graded ring]]
:• [[Involutive ring]]
:• [[Category of rings]]
::• [[Integer|Initial ring]] <math>\mathbb{Z}</math>
::• [[Zero ring|Terminal ring]] <math>0 = \mathbb{Z}_1</math>

'''Related structures'''
:• [[Field (mathematics)|Field]]
::• [[Finite field]]
:• [[Non-associative ring]]
::• [[Lie ring]]
::• [[Jordan ring]]
:• [[Semiring]]
::• [[Semifield]]

| list3name = Commutative
| list3title = [[Commutative algebra]]
| list3style = text-align: left;
| list3 = 
'''[[Commutative ring]]s'''
:• [[Integral domain]]
::• [[Integrally closed domain]]
::• [[GCD domain]]
::• [[Unique factorization domain]]
::• [[Principal ideal domain]]
::• [[Euclidean domain]]
::• [[Field (mathematics)|Field]]
:::• [[Finite field]]
:• [[Composition ring]]
::• [[Polynomial ring]]
::• [[Formal power series ring]]

'''[[Algebraic number theory]]'''
:• [[Algebraic number field]]
:• [[Ring of integers]]
:• [[Algebraic independence]]
:• [[Transcendental number theory]]
:• [[Transcendence degree]]

'''[[Radix|''p''-adic]] number theory and [[Positional notation|decimals]]'''
:• [[Direct limit]]/[[Inverse limit]]
:• [[Zero ring]] <math>\mathbb{Z}_1</math>
:• [[Integers modulo n|Integers modulo ''p''<sup>n</sup>]] <math>\mathbb{Z}/p^n\mathbb{Z}</math>
:• [[Prüfer group#The Prüfer group as a ring|Prüfer ''p''-ring]] <math>\mathbb{Z}(p^\infty)</math>
:• [[Radix|Base]]-''p'' [[Circle group#The circle group as a ring|circle ring]] <math>\mathbb{T}</math>
:• [[Radix|Base]]-''p'' [[integers]] <math>\mathbb{Z}</math>
:• [[Dyadic rational|''p''-adic rational]]s <math>\mathbb{Z}[1/p]</math>
:• [[Radix|Base]]-''p'' [[real number]]s <math>\mathbb{R}</math>
:• [[p-adic integer|''p''-adic integers]] <math>\mathbb{Z}_p</math>
:• [[p-adic number|''p''-adic numbers]] <math>\mathbb{Q}_p</math>
:• [[Solenoid (mathematics)#p-adic solenoids|''p''-adic solenoid]] <math>\mathbb{T}_p</math>

'''[[Algebraic geometry]]'''
:• [[Affine variety]]

| list4name = Noncommutative
| list4title = [[Noncommutative algebra]]
| list4style = text-align: left;
| list4 =
'''[[Noncommutative ring]]s'''
:• [[Division ring]]
:• [[Semiprimitive ring]]
:• [[Simple ring]]
:• [[Commutator (ring theory)|Commutator]]

'''[[Noncommutative algebraic geometry]]'''

'''[[Free algebra]]'''

'''[[Clifford algebra]]'''
:• [[Geometric algebra]]
<!--::• [[Spacetime algebra]] – too application-specific to be of interest in this template-->

'''[[Operator algebra]]'''


))</includeonly><noinclude>
((documentation))
</noinclude>

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Template:(( (view source) (protected)
Template:)) (view source) (protected)
Template:Blue (view source) (template editor protected)
Template:Braces (view source) (semi-protected)
Template:Collapsible lists option (view source) (template editor protected)
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Template:Hlist/styles.css (view source) (protected)
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Module:TableTools (view source) (protected)

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