Www.liegroups.org. ATLAS of Finite Group Representations - V3. Algebraic topology. Algebraic geometry. Algebraic geometry is a branch of mathematics, classically studying zeros of polynomial equations.
Modern algebraic geometry is based on more abstract techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. Algebraic geometry occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex analysis, topology and number theory. Initially a study of systems of polynomial equations in several variables, the subject of algebraic geometry starts where equation solving leaves off, and it becomes even more important to understand the intrinsic properties of the totality of solutions of a system of equations, than to find a specific solution; this leads into some of the deepest areas in all of mathematics, both conceptually and in terms of technique.
In the 20th century, algebraic geometry has split into several subareas. Basic notions[edit] Algebraic structure. The properties of specific algebraic structures are studied in abstract algebra.
The general theory of algebraic structures has been formalized in universal algebra. Category theory is used to study the relationships between two or more classes of algebraic structures, often of different kinds. For example, Galois theory studies the connection between certain fields and groups, algebraic structures of two different kinds. In a slight abuse of notation, the word "structure" can also refer only to the operations on a structure, and not the underlying set itself.
For example, a phrase "we have defined a ring structure (a structure of ring) on the set.