# Commutative Algebra

One important role of commutative algebra is in the foundations of algebraic geometry, through rings of functions on a variety, and generalizations, incorporating nilpotent elements, and also sheaves of rings lying over such a variety (or scheme). Other issues in commutative algebra, such as factorization, also directly relate to number theory. Members of this group study these issues and others, such as the structure of commutative rings.