Modern algebra is yet a further generalization of arithmetic than is classical algebra. It deals with operations that are not necessarily those of arithmetic and that apply to elements that are not necessarily numbers. The elements are members of a set and are classed as a group, a ring, or a field according to the axioms that are satisfied under the particular operations defined for the elements. Among the important concepts of modern algebra are those of a matrix and of a vector space.
The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.