Algebra, an immense area of mathematics, is the study of mathematical symbols and the rules for regulating these symbols. At West Virginia University, we conduct research in commutative algebra and higher (or derived) algebra.
Commutative algebra forms the foundation of algebraic geometry and finds applications in various areas including algebraic number theory, combinatorics, and homotopy theory. The subject of higher algebra is a blend of ideas from algebraic topology with methods of category theory and classical algebra. It has connections with quantum field theory, algebraic andarithmetic geometry. We use techniques of homological algebra, representation theory, higher (or derived) algebra to study both commutative and derived rings along with their modules, and algebraic K-theory.