Category:Definitions/Ring Theory
This category contains definitions related to Ring Theory.
Related results can be found in Category:Ring Theory.
Ring Theory is a branch of abstract algebra which studies rings and other related algebraic structures.
Subcategories
This category has the following 16 subcategories, out of 16 total.
B
C
D
E
F
G
I
L
N
O
P
S
T
Pages in category "Definitions/Ring Theory"
The following 200 pages are in this category, out of 204 total.
(previous page) (next page)A
- Definition:Additive Function on UFD
- Definition:Additive Group
- Definition:Additive Identity
- Definition:Additive Inverse
- Definition:Additive Semiring
- Definition:Additive Semiring Axioms
- Definition:Additive Semiring/Axioms
- Definition:Additive Subgroup
- Definition:Algebra Defined by Ring Homomorphism
- Definition:Algebraic Element of Ring Extension
- Definition:Algebraic over Integral Domain
- Definition:Annihilator of Ring
- Definition:Antihomomorphism/Ring Antihomomorphism
- Definition:Artinian Ring
- Definition:Ascending Chain Condition on Ideals
- Definition:Ascending Chain Condition/Ideals
- Definition:Associate
- Definition:Associate/Commutative Ring
- Definition:Associate/Integral Domain
- Definition:Associate/Integral Domain/Definition 1
- Definition:Associate/Integral Domain/Definition 2
- Definition:Atom (Ring Theory)
C
- Definition:Cancellable Semiring
- Definition:Category of Rings
- Definition:Category of Rings with Unity
- Definition:Center (Abstract Algebra)
- Definition:Center (Abstract Algebra)/Ring
- Definition:Center of Ring
- Definition:Centralizer
- Definition:Characteristic of Ring
- Definition:Characteristic of Ring/Definition 1
- Definition:Characteristic of Ring/Definition 2
- Definition:Characteristic of Ring/Definition 3
- Definition:Common Divisor
- Definition:Commutative Algebra (Mathematical Branch)
- Definition:Commutative and Unitary Ring
- Definition:Commutative and Unitary Ring Axioms
- Definition:Commutative and Unitary Ring/Axioms
- Definition:Commutative Division Ring
- Definition:Commutative Ring
- Definition:Commutative Ring with Unity
- Definition:Commutative Semiring
- Definition:Commutator/Ring
- Definition:Completely Additive Function
D
F
G
- Definition:Generated Subring
- Definition:Generator of Division Subring
- Definition:Generator of Ideal of Ring
- Definition:Generator of Ring
- Definition:Generator of Subring
- Definition:Gradation Compatible with Ring Structure
- Definition:Group of Units
- Definition:Group of Units of Ring
- Definition:Group of Units/Ring
- Definition:Group Ring
H
I
- Definition:Ideal of Ring
- Definition:Ideal Theory
- Definition:Idempotent Ring
- Definition:Identity Automorphism
- Definition:Initial Homomorphism from Integers to Ring with Unity
- Definition:Integral Multiple/Rings and Fields
- Definition:Internal Direct Product of Rings
- Definition:Internal Direct Sum of Rings
- Definition:Internal Direct Sum of Rings/Direct Summand
- Definition:Isomorphism (Abstract Algebra)/F-Isomorphism
- Definition:Isomorphism (Abstract Algebra)/Ring Isomorphism
L
M
N
- Definition:Negativity Property
- Definition:Nilpotent Ring Element
- Definition:Nilradical of Ring
- Definition:Nilradical of Ring/Definition 1
- Definition:Nilradical of Ring/Definition 2
- Definition:Noetherian Ring
- Definition:Non-Null Ring
- Definition:Non-Zero-Divisor
- Definition:Nonzero Ring Element
- Definition:Norm/Ring
- Definition:Norm/Ring/Multiplicative
- Definition:Norm/Ring/Submultiplicative
- Definition:Normed Ring
- Normed Vector Space Requires Multiplicative Norm on Division Ring
- Definition:Null Ring
P
- Definition:Polynomial Equation
- Definition:Polynomial Function
- Definition:Polynomial Function/General Definition
- Definition:Polynomial over Ring as Function on Free Monoid on Set
- Definition:Polynomial Ring over Sequence
- Definition:Positive Characteristic
- Definition:Positive Definite (Division Ring)
- Definition:Primal
- Definition:Prime Element of Ring
- Definition:Product Inverse
- Definition:Proper Divisor
- Definition:Proper Element of Ring
- Definition:Proper Subring
- Definition:Proper Zero Divisor
R
- Definition:Reduced Ring
- Definition:Regular Element of Ring
- Definition:Rig
- Definition:Right Zero Divisor
- Definition:Ring (Abstract Algebra)
- Definition:Ring (Abstract Algebra)/Binding Priority
- Definition:Ring (Abstract Algebra)/Ring Addition
- Definition:Ring (Abstract Algebra)/Ring Axioms
- Definition:Ring (Abstract Algebra)/Ring Less Zero
- Definition:Ring (Abstract Algebra)/Ring Product
- Definition:Ring Addition
- Definition:Ring Antihomomorphism
- Definition:Ring Automorphism
- Definition:Ring Direct Product
- Definition:Ring Direct Product/Finite Case
- Definition:Ring Embedding
- Definition:Ring Endomorphism
- Definition:Ring Epimorphism
- Definition:Ring Extension
- Definition:Ring Homomorphism
- Definition:Ring Isomorphism
- Definition:Ring Less Zero
- Definition:Ring Monomorphism
- Definition:Ring Negative
- Definition:Ring of Idempotents
- Definition:Ring of Integers
- Definition:Ring of Mappings
- Definition:Ring Product
- Definition:Ring Product Inverse
- Definition:Ring Subtraction
- Definition:Ring Theory
- Definition:Ring with Unity
- Definition:Ring Zero
- Definition:Ringoid (Abstract Algebra)
- Definition:Root of Mapping
- Definition:Root of Polynomial
S
- Definition:Schreier Domain
- Definition:Semihereditary Ring
- Definition:Semiring (Abstract Algebra)
- Definition:Skew Field
- Definition:Spectrum of Ring
- Definition:Subdomain
- Definition:Submultiplicative Norm on Ring
- Definition:Subring
- Definition:Subsemiring
- Definition:Subtraction
- Definition:Sum of Ideals of Ring
T
- Definition:Topological Division Ring
- Definition:Topological Ring
- Definition:Transcendental
- Definition:Transcendental Element of Ring Extension
- Definition:Transcendental over Integral Domain
- Definition:Trivial Annihilator
- Definition:Trivial Gradation
- Definition:Trivial Homomorphism
- Definition:Trivial Ring
- Definition:Two Ring
