Algebra
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of statements within those systems.
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of statements within those systems. Abstract algebra studies algebraic structures, which consist of a set of mathematical objects together with one or several operations defined on that set. It is a generalization of elementary and linear algebra, since it allows mathematical objects other than numbers and non-arithmetic operations.
The Algebra group studies both commutative and non-commutative structures.
The research in commutative algebra focuses mostly on three areas: Prime characteristic methods using Frobenius endomorphism; local cohomology modules and their finiteness property; and combinatorial methods with applications to various invariants associated with rings and their modules.
The research in non-commutative algebra is conducted in the following areas: non-commutative Noetherian rings and their modules; especially simple infinite dimensional Noetherian non-commutative algebras and various classification problems associated with them; rings of differential operators and D-modules; dimensions (the Krull dimension, the global homological dimension, the Gelfand-Kirillov dimension, the filter dimension); Poisson and Lie algebras; algebras of Poisson differential operators; groups of algebra automorphisms; derivations; graded and filtered algebras; and various properties of elements of rings and associated algebraic objects (like derivations and associated algebras, etc).