Glossary of ring theory
Template:Short description Ring theory is the branch of mathematics in which rings are studied: that is, structures supporting both an addition and a multiplication operation. This is a glossary of some terms of the subject.
For the items in commutative algebra (the theory of commutative rings), see Glossary of commutative algebra. For ring-theoretic concepts in the language of modules, see also Glossary of module theory.
For specific types of algebras, see also: Glossary of field theory and Glossary of Lie groups and Lie algebras. Since, currently, there is no glossary on not-necessarily-associative algebra structures in general, this glossary includes some concepts that do not need associativity; e.g., a derivation.
A
<templatestyles src="Glossary/styles.css" />
-
<dt id="Script error: No such module "delink"." >Amitsur complex
Template:Defn
<dt id="Script error: No such module "delink"." >Artinian
Template:Defn
<dt id="Script error: No such module "delink"." >associate
Template:Defn
<dt id="Script error: No such module "delink"." >automorphism
Template:Defn
Template:Defn
<dt id="Script error: No such module "delink"." >Azumaya
Template:Defn
B
<templatestyles src="Glossary/styles.css" />
-
<dt id="Script error: No such module "delink"." >bidimension
Template:Defn
<dt id="Script error: No such module "delink"." >boolean
Template:Defn
<dt id="Script error: No such module "delink"." >Brauer
Template:Defn
C
<templatestyles src="Glossary/styles.css" />
-
<dt id="Script error: No such module "delink"." >category
Template:Defn
<dt id="Script error: No such module "delink"." >centre
Template:Defn
Template:Defn
Template:Defn
<dt id="Script error: No such module "delink"." >centralizer
Template:Defn
Template:Defn
<dt id="Script error: No such module "delink"." >characteristic
Template:Defn
Template:Defn
<dt id="Script error: No such module "delink"." >change
Template:Defn
<dt id="Script error: No such module "delink"." >Clifford algebra
Template:Defn
<dt id="Script error: No such module "delink"." >coherent
Template:Defn
<dt id="Script error: No such module "delink"." >commutative
Template:Defn
Template:Defn
Template:Defn
Template:Defn
D
<templatestyles src="Glossary/styles.css" />
-
<dt id="Script error: No such module "delink"." >derivation
Template:Defn
Template:Defn
<dt id="Script error: No such module "delink"." >differential
Template:Defn
<dt id="Script error: No such module "delink"." >direct
Template:Defn
<dt id="Script error: No such module "delink"." >divisor
Template:Defn
Template:Defn
<dt id="Script error: No such module "delink"." >division
Template:Defn
<dt id="Script error: No such module "delink"." >domain
Template:Defn
E
<templatestyles src="Glossary/styles.css" />
-
<dt id="Script error: No such module "delink"." >endomorphism
Template:Defn
<dt id="Script error: No such module "delink"." >enveloping algebra
Template:Defn
<dt id="Script error: No such module "delink"." >extension
Template:Defn
<dt id="Script error: No such module "delink"." >exterior algebra
Template:Defn
F
<templatestyles src="Glossary/styles.css" />
-
<dt id="Script error: No such module "delink"." >field
Template:Defn
<dt id="Script error: No such module "delink"." >filtered ring
Template:Defn
<dt id="Script error: No such module "delink"." >finitely generated
Template:Defn
Template:Defn
<dt id="Script error: No such module "delink"." >finitely presented
Template:Defn
<dt id="Script error: No such module "delink"." >free
Template:Defn
Template:Defn
Template:Defn
Template:Defn
G
<templatestyles src="Glossary/styles.css" />
-
<dt id="Script error: No such module "delink"." >graded
Template:Defn
<dt id="Script error: No such module "delink"." >generate
Template:Defn
H
<templatestyles src="Glossary/styles.css" />
-
<dt id="Script error: No such module "delink"." >hereditary
Template:Defn
I
<templatestyles src="Glossary/styles.css" />
-
<dt id="Script error: No such module "delink"." >ideal
Template:Defn
<dt id="Script error: No such module "delink"." >idempotent
Template:Defn
<dt id="Script error: No such module "delink"." >integral domain
Template:Defn
<dt id="Script error: No such module "delink"." >invariant
Template:Defn
<dt id="Script error: No such module "delink"." >irreducible
Template:Defn
J
<templatestyles src="Glossary/styles.css" />
-
<dt id="Script error: No such module "delink"." >Jacobson
Template:Defn
Template:Defn
K
<templatestyles src="Glossary/styles.css" />
-
<dt id="Script error: No such module "delink"." >kernel
Template:Defn
<dt id="Script error: No such module "delink"." >Köthe
Template:Defn
L
<templatestyles src="Glossary/styles.css" />
-
<dt id="Script error: No such module "delink"." >local
Template:Defn
Template:Defn
M
<templatestyles src="Glossary/styles.css" />
-
<dt id="Script error: No such module "delink"." >minimal and maximal
Template:Defn
Template:Defn
<dt id="Script error: No such module "delink"." >matrix
Template:Defn
Template:Defn
<dt id="Script error: No such module "delink"." >monoid
Template:Defn
<dt id="Script error: No such module "delink"." >Morita
Template:Defn
N
<templatestyles src="Glossary/styles.css" />
-
<dt id="Script error: No such module "delink"." >nearring
Template:Defn
<dt id="Script error: No such module "delink"." >nil
Template:Defn
Template:Defn
Template:Defn
<dt id="Script error: No such module "delink"." >nilpotent
Template:Defn
Template:Defn
Template:Defn
Template:Defn
<dt id="Script error: No such module "delink"." >Noetherian
Template:Defn
<dt id="Script error: No such module "delink"." >null
Template:Defn
O
<templatestyles src="Glossary/styles.css" />
-
<dt id="Script error: No such module "delink"." >opposite
Template:Defn
<dt id="Script error: No such module "delink"." >order
Template:Defn
<dt id="Script error: No such module "delink"." >Ore
Template:Defn
P
<templatestyles src="Glossary/styles.css" />
-
<dt id="Script error: No such module "delink"." >perfect
Template:Defn
<dt id="Script error: No such module "delink"." >polynomial
Template:Defn
Template:Defn
<dt id="Script error: No such module "delink"." >prime
Template:Defn
Template:Defn
Template:Defn
Template:Defn
<dt id="Script error: No such module "delink"." >primitive
Template:Defn
Template:Defn
<dt id="Script error: No such module "delink"." >principal
Template:Defn
<dt id="Script error: No such module "delink"." >principal
Template:Defn
Template:Defn
Q
<templatestyles src="Glossary/styles.css" />
-
<dt id="Script error: No such module "delink"." >quasi-Frobenius
Template:Defn
Template:Defn
R
<templatestyles src="Glossary/styles.css" />
-
<dt id="Script error: No such module "delink"." >radical
Template:Defn
<dt id="Script error: No such module "delink"." >ring
Template:Defn
Template:Defn
Template:Defn
<dt id="Script error: No such module "delink"." >rng
Template:Defn
Template:Defn
S
<templatestyles src="Glossary/styles.css" />
-
<dt id="Script error: No such module "delink"." >self-injective
Template:Defn
<dt id="Script error: No such module "delink"." >semiperfect
Template:Defn
<dt id="Script error: No such module "delink"." >semiprimary
Template:Defn
<dt id="Script error: No such module "delink"." >semiprime
Template:Defn
Template:Defn
<dt id="Script error: No such module "delink"." >semiprimitive
Template:Defn
<dt id="Script error: No such module "delink"." >semiring
Template:Defn
<dt id="Script error: No such module "delink"." >semisimple
Template:Defn
<dt id="Script error: No such module "delink"." >separable
Template:Defn
<dt id="Script error: No such module "delink"." >serial
Template:Defn
<dt id="Script error: No such module "delink"." >Severi–Brauer
Template:Defn
<dt id="Script error: No such module "delink"." >simple
Template:Defn
Template:Defn
<dt id="Script error: No such module "delink"." >singular submodule
Template:Defn
<dt id="Script error: No such module "delink"." >subring
Template:Defn
<dt id="Script error: No such module "delink"." >symmetric algebra
Template:Defn
Template:Defn
<dt id="Script error: No such module "delink"." >Sylvester domain
Template:Defn
T
<templatestyles src="Glossary/styles.css" />
-
<dt id="Script error: No such module "delink"." >tensor
Template:Defn
Template:Defn
<dt id="Script error: No such module "delink"." >trivial
Template:Defn
Template:Defn
U
<templatestyles src="Glossary/styles.css" />
-
<dt id="Script error: No such module "delink"." >unit
Template:Defn
<dt id="Script error: No such module "delink"." >unity
Template:Defn
<dt id="Script error: No such module "delink"." >unique
Template:Defn
<dt id="Script error: No such module "delink"." >uniserial
Template:Defn
V
<templatestyles src="Glossary/styles.css" />
-
<dt id="Script error: No such module "delink"." >von Neumann regular element
Template:Defn
Template:Defn
W
<templatestyles src="Glossary/styles.css" />
-
<dt id="Script error: No such module "delink"." >Wedderburn–Artin theorem
Template:Defn
Script error: No such module "anchor".
Z
<templatestyles src="Glossary/styles.css" />
-
<dt id="Script error: No such module "delink"." >zero
Template:Defn
See also
Citations
<templatestyles src="Reflist/styles.css" />
Script error: No such module "Check for unknown parameters".
References
<templatestyles src="Refbegin/styles.css" />
- Script error: No such module "citation/CS1".
- Script error: No such module "citation/CS1".
- Template:EGA
- Script error: No such module "citation/CS1".
- Script error: No such module "citation/CS1".
- Script error: No such module "citation/CS1".