From Simple English Wikipedia, the free encyclopedia
Abstract algebra
is a part of
math
which studies
algebraic structures
. These include:
It is normal to build a theory on one kind of structure, like
group theory
or
category theory
.
The purpose of the theory of each concept is to organize the precise definition of the concept, examples of it, its substructures, the ways to relate different examples of the concept algebraically (these are called
morphisms
in some cases), and the concept's applications, both inside its own theory and outside in other areas of mathematics.
During history, different fields of mathematics have used
algebras
. Algebras are about finding or specifying rules on how to calculate with certain mathematical formulas and expressions. Another algebra (which is not
abstract
) is
elementary algebra
, for example.
- Allenby, R. B. J. T. (1991).
Rings, fields, and groups : an introduction to abstract algebra
(2nd ed.). London: E. Arnold.
ISBN
978-0-340-54440-2
.
- Hartman, Philip (January 2002).
Ordinary differential equations
(2nd ed.). Philadelphia: Society for Industrial and Applied Mathematics.
ISBN
978-0-89871-510-1
.
- Burris, Stanley N.; Sankappanavar, H. P. (1999) [1981], A Course in Universal Algebra
- Gilbert, Jimmie (2005).
Elements of modern algebra
(6th ed.). Belmont, CA: Thomson Brooks/Cole.
ISBN
978-0-534-40264-8
.
- Lang, Serge (21 June 2005).
Algebra
(Revised Third ed.). New York.
ISBN
978-0-387-95385-4
.
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link
)
- Sethuraman, B. A. (1997).
Rings, fields, and vector spaces : an introduction to abstract algebra via geometric constructability
. New York: Springer.
ISBN
978-0-387-94848-5
.
- Whitehead, C. (6 December 2002).
Guide to abstract algebra
(2nd ed.). Basingstoke: Palgrave.
ISBN
978-0-333-79447-0
.
- Nicholson, W. Keith (20 March 2012).
Introduction to abstract algebra
(4th ed.). Hoboken: John Wiley & Sons.
ISBN
978-1-118-13535-8
.
- John R. Durbin (1992) Modern Algebra : an introduction, John Wiley & Sons