Category:Ring Theory
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This category contains results about Ring Theory.
Definitions specific to this category can be found in Definitions/Ring Theory.
Ring Theory is a branch of abstract algebra which studies rings and other related algebraic structures.
Subcategories
This category has the following 61 subcategories, out of 61 total.
A
- Artinian Rings (empty)
B
- Boolean Rings (6 P)
- Bézout Domains (1 P)
C
- Cyclotomic Rings (9 P)
D
- Direct Sums of Rings (2 P)
E
- Examples of Zero Divisors (4 P)
F
G
- Graded Rings (empty)
- Group Rings (1 P)
I
- Ideals of Rings (1 P)
L
M
N
- Nilpotence (1 P)
- Nilpotent Ring Elements (4 P)
- Normed Rings (empty)
O
P
- Prime Elements of Rings (1 P)
- Proper Divisors (1 P)
Q
R
- Ring Commutators (empty)
- Ring Direct Products (1 P)
- Ring Endomorphisms (1 P)
- Ring Epimorphisms (13 P)
- Ring Extensions (empty)
- Ring Zero is Unique (4 P)
- Rings of Sequences (2 P)
- Roots of Mappings (empty)
- Roots of Polynomials (empty)
S
- Semirings (2 P)
- Submultiplicative Functions (1 P)
T
- Trivial Rings (4 P)
U
- Units of Rings (6 P)
Z
Pages in category "Ring Theory"
The following 87 pages are in this category, out of 87 total.
C
D
E
I
- Ideal Contains Extension of Contraction
- Ideal is Bimodule over Ring/Ring is Bimodule over Ring
- Ideal is Contained in Contraction of Extension
- Idempotent Elements of Ring with No Proper Zero Divisors
- Increasing Union of Ideals is Ideal
- Increasing Union of Ideals is Ideal/Chain
- Integral Domain is Reduced Ring
- Integral Multiple Distributes over Ring Addition
- Integral Multiple of Ring Element
- Integral Multiple of Ring Element/General Result
- Inverse of Central Unit of Ring is in Center
- Inverse of Unit in Centralizer of Ring is in Centralizer
L
- Left Module Does Not Necessarily Induce Right Module over Ring
- Left Module induces Right Module over same Ring iff Actions are Commutative
- Left Module over Commutative Ring induces Bimodule
- Left Module over Commutative Ring induces Right Module
- Left Module over Ring Induces Right Module over Opposite Ring
N
P
R
- Radical of Power of Prime Ideal
- Radical of Prime Ideal
- Right Module Does Not Necessarily Induce Left Module over Ring
- Right Module induces Left Module over same Ring iff Actions are Commutative
- Right Module over Commutative Ring induces Bimodule
- Right Module over Commutative Ring induces Left Module
- Right Module over Ring Induces Left Module over Opposite Ring
- Ring by Idempotent
- Ring Homomorphism by Idempotent
- Ring is Bimodule over Ring
- Ring is Left Module over Ring
- Ring is not Empty
- Ring is Right Module over Ring
- Ring Less Zero is Semigroup for Product iff No Proper Zero Divisors
- Ring Negative is Unique
- Ring of Idempotents is Idempotent Ring
- Ring of Idempotents of Commutative and Unitary Ring is Boolean Ring
- Ring Product with Zero
- Ring Subtraction equals Zero iff Elements are Equal
- Ring Zero is Idempotent
- Ring Zero is not Cancellable
- Ring Zero is Unique