concepts in abstract algebra
The aim of this entry is to present a list of the key operators used in abstract algebra. Each entry in the list (or will in the future) to the corresponding PlanetMath entry where the object is presented in greater detail. For convenience, this list also presents the encouraged notation to use (at PlanetMath) for these objects.
- •
group, subgroup
- •
normal subgroup
- •
cyclic group
- •
group algebra
- •
Galois group
- •
Polish group
- •
G-Set (http://planetmath.org/G-Set)
- •
groupoid
group
- •
groupoid
- •
semigroup
- •
monoid
- •
generator
, generate
- •
commutator
(http://planetmath.org/DerivedSubgroup)
- •
cyclic group generated by an element
- •
ring, subring
- •
polynomial ring
- •
, ideal
- •
quotient ring
- •
localization
of at
- •
integral domain
- •
division ring
- •
ring group
- •
, field
- •
normalizer
of a subgroup
- •
centralizer
of an element
- •
center of a group (or centre of a group)
- •
normal subgroup
- •
characteristic subgroup
- •
quotient group
- •
normal closure
- •
left coset
and right coset (http://planetmath.org/Coset) respectively
- •
element, unit, unity, inverse
, identity
- •
nilpotent
- •
idempotent
- •
module, submodule
- •
homomorphism
, homomorphy
- •
isomorphism
, isomorphy, isomorphic
- •
monomorphism
, epimorphism
- •
endomorphism
- •
automorphism
General Algebras and Algebroids
- •
Universal algebras
- •
superalgerbas
- •
F-algebras
- •
double algebras
- •
Quantum Operator algebras
- •
general algebras
- •
higher dimensional algebras
- •
logic algebras
- •
quantum logic
algebras
Title | concepts in abstract algebra |
Canonical name | ConceptsInAbstractAlgebra |
Date of creation | 2013-03-22 14:42:38 |
Last modified on | 2013-03-22 14:42:38 |
Owner | matte (1858) |
Last modified by | matte (1858) |
Numerical id | 26 |
Author | matte (1858) |
Entry type | Topic |
Classification | msc 55-00 |
Classification | msc 18-00 |
Classification | msc 16-00 |
Classification | msc 13-00 |
Classification | msc 20-00 |
Classification | msc 15-00 |
Synonym | classes of algebras |
Synonym | examples of algebras |