**Date & Time:** Tuesday, April 09, 2013, 15:30-17:00.

**Venue:** Ramanujan Hall

**Title:** The Eakin-Sathaye Theorem about reductions of ideals

**Speaker:**Shreedevi Masuti, IIT Bombay

**Abstract:** We will present a proof of the Eakin-Sathaye Theorem: If I is an ideal of a local ring (R,m) with infinite R/m and I^n can be generated by at most (n+r)!/r!n!-1 elements then there exist a_1,a_2, ... , a_r in I so that I^n=(a_1a_2,..., a_r)I^{n-1}. We will follow the proof given by G. Caviglia using Green's hyperplane section theorem.