Website owner:  James Miller

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Groups, Rings, Integral Domains and Fields

Select from the following:

Functions, mappings, maps, transformations, operators. Onto, one-to-one, surjective, injective, bijective, identity, product, inverse functions. Group of transformations on a set. Permutation. Symmetric group Sn

Congruence, residue classes of integers modulo m

Products, quotients and roots of complex numbers in polar form, primitive roots of unity

Modern, abstract mathematics

Binary operations

Groups, subgroups, complexes, cosets, transforms, normal subgroups, quotient groups, commutators, composition series, isomorphisms, homomorphisms, automorphisms

Permutations, cyclic permutations (cycles), permutation groups, transpositions. Even and odd permutations. Symmetric and alternating groups. Decomposition of a permutation group into cycles and a product of transpositions.


Conjugates, conjugate classes, automorphisms, normal subgroups, quotient groups, homomorphic mapping of groups

The symmetric group on four letters, S4

The dihedral group of the square


Ideals, quotient rings, homomorphisms

Integral domains and fields

Axioms satisfied by rings, integral domains and fields

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