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Algebra Seminar
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Vahap Erdogdu
University of Sydney

Coprime packedness and set-theoretic complete intersections of ideals in polynomial rings

Friday 7th November, 12:05-12:55pm, Carslaw 173.

Let K be a field and P a height two prime ideal of the polynomial ring K[X,Y,Z]. A well-known conjecture states that P is a set-theoretic complete intersection. Motivated by this, in this talk I will consider rings R over which the polynomial ring R[X] has the property that each proper prime ideal of it is a set-theoretic complete intersection. To do so I will first define and examine rings which are coprimely packed, a notion closely related to that of set-theoretic complete intersection.