In this paper, we introduce the notion of p_ g pg-ideals and p_ g pg-cycles, which inherits
nice properties of integrally closed ideals on rational singularities. As an application, we …

The main aim of this paper is to classify Ulrich ideals and Ulrich modules over two-
dimensional Gorenstein rational singularities (rational double points) from a geometric point …

Let be an excellent two-dimensional normal local domain. In this paper, we study the elliptic
and the strongly elliptic ideals of A with the aim to characterize elliptic and strongly elliptic …

The notion of p g-ideals for normal surface singularities has been proved to be very useful.
On the other hand, the core of ideals has been proved to be very important concept and also …

In this paper we consider the problem of explicitly finding canonical ideals of one-
dimensional Cohen–Macaulay local rings. We show that Gorenstein ideals contained in a …

Let p be the unique singularity of a normal two-dimensional Stein space V. Let m be the
maximal ideal in $ _V {\mathcal {O} _p} $, the local ring of germs of holomorphic functions at …

Hilbert–Kunz multiplicity is known to be a very mysterious invariant of a ring or an ideal. We
will show a very beautiful formula on Hilbert–Kunz multiplicity for integrally closed ideals in …

We introduce the the normal reduction number of two-dimensional normal singularities and
prove that elliptic singularity has normal reduction number two. We also prove that for a two …

A conjecture of Hirose, Watanabe, and Yoshida offers a characterization of when a standard
graded strongly-regular ring is Gorenstein, in terms of an-pure threshold. We prove this …

The notions of F-regularity and F-purity for rings of characteristic p> 0, which are introduced
by Hochster and Huneke [HH1] and Hochster and Roberts [HR], respectively, are now …