In this paper, starting with a commutative ring R and a proper ideal I⊂ R, we construct and
study a new ring denoted by R⋈ I. In particular, we prove that if R is a CM local ring, then R⋈ …

This book is a slightly extended elaboration of a course on commutative ring theory and
plane algebraic curves that I gave several times at the University of Regensburg to students …

We prove two formulae that express the Alexander polynomial Δ\spC of several variables of
a plane curve singularity C in terms of the ring O\sbC of germs of analytic functions on the …

Reports on the application of the notion of the integral with respect to the Euler characteristic
over the projectivization of the space of germs of functions, for computing the Poincare …

The notion of integration with respect to the Euler characteristic and its generalizations are
discussed: integration over the infinite-dimensional spaces of arcs and functions, motivic …

In a one-dimensional local ring R with finite integral closure each nonzerodivisor has a
value in N d, where d is the number of maximal ideals in the integral closure. The set of …

The canonical module of a one-dimensional reduced local ring Page 1 COMMUNICATIONS
IN ALGEBRA, 25(9), 2939-2965 (1997) THE CANONICAL MODULE OF A ONE-DIMENSIONAL …

Abstract We compute the Heegaard Floer link homology of algebraic links in terms of the
multi-variate Hilbert function of the corresponding plane curve singularities. The main result …

We construct the analytic lattice cohomology associated with the analytic type of any
complex normal surface singularity. It is the categorification of the geometric genus of the …

Value semigroups of non irreducible singular algebraic curves and their fractional ideals are
submonoids of $\mathbb Z^ n $ that are closed under infimums, have a conductor and fulfill …