2019/11/11 by Das, Suprajo
#Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1911.04531
The notion of ε-multiplicity was originally defined by Ulrich and Validashti as a limsup and they used it to detect integral dependence of modules. It is important to know if it can be realized as a limit. In this article we show that the relative epsilon multiplicity of reduced standard graded algebras over an excellent local ring exists as a limit. We also obtain some important special cases of Cutkosky's results concerning ε-multiplicity, as corollaries of our main theorem.