Integral closure has played a role in number theory and algebraic geometry since the
nineteenth century, but a modern formulation of the concept for ideals perhaps began with …

Let $ T $ be a multigraded ring defined over a local ring $(A,\mathfrak {m}) $. This paper
deals with the question how the Cohen-Macaulay property of $ T $ is related to that of its …

Joint reductions and mixed multiplicities are relatively new concepts and there is very little
about them in the literature. We provide some background in the first two sections. Some of …

The aim of this paper is to extend and unify several results concerning complete ideals in 2-
dimensional regular local rings by using the theory of joint reductions and mixed …

This paper is a survey on major results on Hilbert functions of multigraded algebras and
mixed multiplicities of ideals, including their applications to the computation of Milnor …

Abstract Let f:(ℂ n, 0)→(ℂ p, 0) be a complete intersection with an isolated singularity at the
origin. We give a lower bound for the Milnor number of f in terms of the mixed multiplicities of …

Let $(A,\frak m) $ be a noetherian local ring with maximal ideal $\frak {m} $ and infinite
residue field $ k= A/\frak {m}. $ Let $ J $ be an $\frak m $-primary ideal, $ I_1,\ldots, I_s …

We survey some of the major results about normal Hilbert polynomials of ideals. We discuss
a formula due to Lipman for complete ideals in regular local rings of dimension two …

Mixed multiplicities and the multiplicity of Rees modules of reductions Page 1 Journal of Algebra
and Its Applications Vol. 18, No. 9 (2019) 1950176 (13 pages) c© World Scientific Publishing …

Let $ S $ be an $\mathbf {N}^ d $-graded algebra over a noetherian ring and a finitely
generated $\mathbf {N}^ d $-graded $ S $-module $ M $. This paper will study the …