Felix Gotti, Massachusetts Institute of Technology

**Date**: Wednesday, February 22, 5:00 pm.

**Abstract**

An integral domain R is atomic if each nonzero nonunit of R factors into irreducibles. Also, an integral domain satisfies the ascending chain condition on principal ideals (ACCP) if every increasing sequence of principal ideals (under inclusion) becomes constant from one point on. Noetherian domains and Krull domains are important classes of integral domains satisfying the ACCP. It is well-known that every integral domain satisfying the ACCP is atomic. Examples of atomic domains that do not satisfy the ACCP are notoriously hard to construct. The first of such examples was constructed by A. Grams back in 1974. In this talk we will discuss some of the known constructions of atomic domains that do not satisfy the ACCP. Throughout the talk, we will also discuss the property of being atomic and that of satisfying the ACCP in the more general setting of commutative and cancellative monoids

**Place**: Celis multipurpose room- C-116

**Research interest Dr. Gotti**

The study of the phenomenon of non-uniqueness of factorizations into irreducibles in integral domains and atomic monoids using techniques of combinatorics, linear algebra, and number theory. He has published over 40 articles.

**Note**: speaker will be available to the entire community for questions and to socialize on

- Wednesday 22, 3:30 – 5:00 pm at Celis 202
- Thursday 23, 9:00 – 10:30 am at Celis 119
- Friday 24 9:30 – 11:00 am at Celis 206