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, subgroup

• Polish group

• G-Set (http://planetmath.org/G-Set)

• groupoid group

• $\mathcal{G}$ groupoid

• monoid

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

• $\langle g\rangle$ cyclic group generated by an element

• $R$ ring, subring

• $I$, $\mathfrak{a}$ ideal

• $R/I$ quotient ring

• $S^{-1}R$ localization of $R$ at $S$

• $D$ integral domain

• $F$, $K$ field

• $N_{G}(H)$ normalizer of a subgroup

• $C(a)$ centralizer of an element

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

• $H\triangleleft G$ normal subgroup

• $H\operatorname{char}G$ characteristic subgroup

• $G/H$ quotient group

• $\langle S^{G}\rangle$ normal closure

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

• element, unit, unity, inverse, identity

• $M$ module, submodule

• homomorphism, homomorphy

• isomorphism, isomorphy, isomorphic

• automorphism

General Algebras and Algebroids

• superalgerbas

• F-algebras

• double algebras

• general 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