Topology Seminar-Ideals in Z[x]

Time and Place: Tuesday April 28, 4:45-5:45;  Phil. 510

Speaker: Rashik Khan (GWU)
 

Title: Ideals in Z[x]
 

Abstract: The ring of polynomials Z[X] is not a principal ideal domain, making the categorization of its ideals nontrivial. In this presentation, we prove classical results in abstract algebra such as Gauss' Lemma and Hilbert's Basis Theorem to deduce properties of Z[X] and determine the structure of its ideals. Special attention is provided to prime and maximal ideals. The results are general and can be applied to polynomial rings in one indeterminate over arbitrary principal ideal domains.