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单词 ConceptsInAbstractAlgebra
释义

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.

  • G group, subgroupMathworldPlanetmathPlanetmath

  • normal subgroupMathworldPlanetmath

  • cyclic groupMathworldPlanetmath

  • group algebraMathworldPlanetmath

  • Galois group

  • Polish group

  • G-Set (http://planetmath.org/G-Set)

  • groupoidPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath group

  • 𝒢 groupoid

  • semigroupPlanetmathPlanetmath

  • monoid

  • generatorPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath, generate

  • [a,b] commutatorMathworldPlanetmathPlanetmath (http://planetmath.org/DerivedSubgroup)

  • g cyclic group generated by an element

  • R ring, subring

  • polynomial ringMathworldPlanetmath

  • I, 𝔞 ideal

  • R/I quotient ringMathworldPlanetmath

  • S-1R localizationMathworldPlanetmath of R at S

  • D integral domainMathworldPlanetmath

  • division ring

  • ring group

  • F, K field

  • NG(H) normalizerMathworldPlanetmath of a subgroup

  • C(a) centralizerMathworldPlanetmath of an element

  • Z(G) center of a group (or centre of a group)

  • HG normal subgroup

  • HcharG characteristic subgroup

  • G/H quotient groupMathworldPlanetmath

  • SG normal closurePlanetmathPlanetmath

  • aH,Ha left cosetMathworldPlanetmath and right coset (http://planetmath.org/Coset) respectively

  • element, unit, unity, inverseMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath, identityPlanetmathPlanetmath

  • nilpotentPlanetmathPlanetmathPlanetmath

  • idempotentMathworldPlanetmathPlanetmath

  • M module, submodule

  • homomorphismMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath, homomorphy

  • isomorphismMathworldPlanetmathPlanetmath, isomorphy, isomorphic

  • monomorphismMathworldPlanetmathPlanetmathPlanetmath, epimorphismMathworldPlanetmath

  • endomorphism

  • automorphism

General Algebras and Algebroids

  • Universal algebrasMathworldPlanetmathPlanetmath

  • superalgerbas

  • F-algebras

  • double algebras

  • Quantum Operator algebrasPlanetmathPlanetmathPlanetmath

  • general algebras

  • higher dimensional algebrasPlanetmathPlanetmath

  • logic algebras

  • quantum logicPlanetmathPlanetmath algebrasMathworldPlanetmathPlanetmath

Titleconcepts in abstract algebra
Canonical nameConceptsInAbstractAlgebra
Date of creation2013-03-22 14:42:38
Last modified on2013-03-22 14:42:38
Ownermatte (1858)
Last modified bymatte (1858)
Numerical id26
Authormatte (1858)
Entry typeTopic
Classificationmsc 55-00
Classificationmsc 18-00
Classificationmsc 16-00
Classificationmsc 13-00
Classificationmsc 20-00
Classificationmsc 15-00
Synonymclasses of algebras
Synonymexamples of algebras
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