Factoring Formal Power Series over Z

09/30/2014 - 12:15pm
09/30/2014 - 1:10pm
Speaker: 
Jesse Elliott (California State University, Channel Islands)
Abstract: 

The polynomial (1+X)(2+X) is reducible as a polynomial over the integers but is irreducible as a formal power series over the integers.  On the other hand, the polynomial 6+X is irreducible as a polynomial over the integers but is reducible as a formal power series over the integers.  How does 6+X factor as a product of formal power series?  More generally, how does one represent a given polynomial over the integers as a product of irreducible formal power series?  We will provide a complete answer to this question.  The solution involves the ring of p-adic integers for primes p.

Where: 
MDSL 126