### MATH 5020: Topics in Algebra

**Description:** Advanced topics chosen from group theory, ring theory, number theory, Lie theory, combinatorics, commutative algebra, algebraic geometry, homological algebra, and representation theory. With change of content, this course may be repeated to a maximum of twelve credits.

**Prerequisites:** MATH 5211.

**Credits:** 3

### MATH 5020 - Section 1: Introduction to Commutative Algebra

**Description:** Commutative Algebra, the study of commutative rings and their modules, emerged as a definite area of mathematics at the beginning of the twentieth century. Its origins lie in the works of eminent mathematicians such as Kronecker, Dedekind, Hilbert and Emmy Noether who sought to develop a solid foundation for number theory. Later, the field was enriched by its relation to modern algebraic geometry, topology, homological algebra, and combinatorics. Today commutative algebra is a deep and beautiful area of study in its own right, which both draws on, and is applicable to, all the disciplines that contributed to its development. In this course we will study the fundamental notions and methods of research of commutative algebra. Topics will include: basic module and ideal notions and constructions (such as prime ideals, zero-divisors, localizations, primary decomposition, integral dependence, completions, and dimension theory), special types of rings (such as valuation rings, Krull domains, Noetherian rings, Artinian rings, and coherent rings), and homological algebra aspects of commutative algebra (such as projectivity, flatness, grade, and factorization properties). Other topics may be introduced as time allows.

**Offered:** Fall

**Credits:** 3

**Sections: **Fall 2012 on Storrs Campus

PSCourseID | Course | Sec | Comp | Time | Room | Instructor |
---|---|---|---|---|---|---|

06179 | 5020 | 001 | Lecture | TuTh 12:30:00 PM-1:45:00 PM | MSB117 | Glaz, Sarah |