View Proposal #497
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| ID | 497 |
|---|---|
| First Name | Kevin |
| Last Name | Bombardier |
| Institution | University of Iowa |
| Speaker Category | graduate student |
| Title of Talk | An Exploration of Factorization: Mathematical Atoms |
| Abstract | The mathematical system of the integers has many useful properties. One of these is unique factorization. For example, we can write the number 14 in a unique way: 14 = 2 * 7. However, the numbers 2 and 7 cannot be factored into "smaller pieces" in a nontrivial way. So in this sense, they could be called atoms of this mathematical system. Other mathematical systems usually do not have all of the nice properties that the integers do. Some useful properties can still be salvaged in certain cases. An atomic domain is a special mathematical system where its members have a factorization into a product of atoms. However, despite the ability to still factor elements into atoms, some are not as well-behaved as the integers were. For example, there are atomic domains where elements have an infinite number of distinct factorizations! We will discuss some important cases of these atomic domains. Of particular interest will be an atomic domain that only has finitely many atoms. |
| Subject area(s) | Commutative Ring Theory, Algebra |
| Suitable for undergraduates? | Y |
| Day Preference | SaturdayMild |
| Computer Needed? | Y |
| Bringing a laptop? | Y |
| Overhead Needed? | N |
| Software requests | |
| Special Needs | |
| Date Submitted | 08/28/2018 |
| Year | 2018 |