The abstract algebra is the branch of mathematics that deals with various algebraic structures such as groups , rings , bodies , modules , and not least the algebras busy and examined their properties. The term "abstract" algebra is used to distinguish it from other sub-areas of mathematics, which, for historical reasons, are also referred to as algebra , such as elementary algebra in school mathematics.
In the history of mathematics, algebraic structures first appeared in other sub-areas of mathematics, were then specified axiomatically and finally examined as independent structures in abstract algebra. Therefore abstract algebra has many connections to all branches of mathematics. Through the abstract approach, for example, superordinate symmetries can be discovered, which then exist in several, actually very different objects. A modern approach is category theory . Abstract algebra is used, for example, in representation theory or in schemes .
- dtv-Atlas zur Mathematik , Vol. 1, 2nd edition 1976, p. 70 ff.
- Robin Hartshorne : Algebraic Geometry. Graduate Texts in Mathematics. Springer-Verlag, New York 1977, ISBN 0-387-90244-9 .