Paul Pollack: Stretching, the truth about nonunique factorization (NTWS 201)
Channel: Number Theory Web Seminar
Date: 03/03/2024

Abstract: Number theorists learn at their mother's knee that unique factorization fails in \Z[\sqrt{-5}]. Less well-known is that \Z[\sqrt{-5}] exhibits only a "half-failure" of unique factorization: while two factorizations into irreducibles of the same element need not agree up to unit factors, their lengths (number of factors) does always agree. This is a special case of a 1960 result of Leonard Carlitz. I will discuss offshoots of Carlitz's theorem. Particular attention will be paid to certain questions of Coykendall regarding "elasticity" of orders in quadratic number fields.

Link to slides, see slides 23 and 36 for corrections: https://drive.google.com/file/d/1xkeqlyTE1OEPhOmxRCzh3js4o1MagbvM

Number Theory Web Seminar: https://www.ntwebseminar.org

Original air date: 
Thursday, February 29, 2024 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm Indian Standard Time)Friday, March 1, 2024 (12am CST, 3am AEDT, 5am NZDT)