2022/08/01 by Hill, Lindsey, Lynn, Rachel
#13A30 #13B22 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2208.01027
In this paper, we prove a result similar to results of Itoh and Hong-Ulrich, proving that integral closure of an ideal is compatible with specialization by a general element of that ideal for ideals of height at least two in a large class of rings. Moreover, we show integral closure of sufficiently large powers of the ideal is compatible with specialization by a general element of the original ideal. In a polynomial ring over an infinite field, we give a class of squarefree monomial ideals for which the integral closure is compatible with specialization by a general linear form.