2022/2023
Introduction to Commutative Algebra
Type:
Optional course (faculty)
Delivered by:
Faculty of Mathematics
When:
3, 4 module
Open to:
students of all HSE University campuses
Instructors:
Vladimir Zhgoon
Language:
English
ECTS credits:
6
Contact hours:
72
Course Syllabus
Abstract
At its most basic level, algebraic geometry is the study of the geometry of solution sets of polynomial systems of equations. Classically, the coefficients of the polynomial equations are assumed to lie in an algebraically closed field. Considering more general coefficient rings, in particular rings of integers in number fields, one arrives at modern algebraic geometry and algebraic number theory. Commutative algebra provides the tools for answering basic questions about solutions sets of polynomial systems, such as finite gen- eration of the system, existence of solutions in some extension of the coefficient ring, dimension and irreducible components, and smoothness and singularities.