Time: 9h00,Wednesday, May 9, 2018
Location: Room semina 6 Flor, Building A6, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi
Abstract: Let R be a noetherian ring, and I an ideal of R. Let f be a function from the collections of ideals of R to the integers, for example f(J)=dim(R/J), for any ideal J of R. Many statements in commutative algebra have the form: The function mapping n to f(I^n) (where n>0), is eventually given by a polynomial of n, for every R and every I. We discuss some of these statements and relevant problems, starting from the classical results due to Hilbert, Serre, Brodmann, etc.