Algebra, an immense area of mathematics, is the study of mathematical symbols and the rules for regulating these symbols. At WVU, we conduct research in commutative algebra. We focus on commutative rings and modules over them by using homological and representation theoretical techniques. The theory of commutative algebra stems from the work of eminent mathematicians such as David Hilbert and Emmy Noether, and it plays an important role in algebraic number theory and complex analysis. The field was enriched by its relation to several areas of mathematics including combinatorics, homological algebra, mathematical physics, representation theory and modern research areas such as algebraic graph theory and algebraic topology. Commutative algebra is one of the essential foundations of modern algebraic geometry. It is the main tool to study the theory of schemes.