In the present paper, we study the Dao numbers $\mathfrak {d} _1 (I),\mathfrak {d} _2 (I) $
and $\mathfrak {d} _3 (I) $ of an ideal $ I $ of a Noetherian local ring $(R,\mathfrak {m}, K) …

The so-called Dao numbers are a sort of measure of the asymptotic behaviour of full
properties of certain product ideals in a Noetherian local ring $ R $ with infinite residue field …

Let $ R $ be a finitely $\mathbb {N} $-graded algebra over a Noetherian ring. In this paper
we study the asymptotic behaviour of the so called $ v $-number $\mathrm {w} _P …

For a local ring $(R,\M) $ of infinite residue field and positive depth, we address the question
raised by H. Dao on how to control the asymptotic behaviour of the $\M $-full, full, and …

The notion of v-numbers of homogeneous ideals in a polynomial ring over a field was
introduced in 2020 to study the asymptotic behaviour of the minimum distance of projective …

Let $ R $ be a commutative noetherian ring, $ I, J $ be two ideals of $ R $, $ M $ be an $ R $-
module, and $\mathcal {S} $ be a Serre class of $ R $-modules. A positive answer to the …

Let $ R $ be a Noetherian standard ${\mathbb {N}}^{\thinspace d} $-graded ring and $ M, N
$ finitely generated, ${\mathbb {N}}^{\thinspace d} $-graded $ R $-modules. Let $ I …

On a common generalization of Koszul duality and tilting equivalence Page 1 Advances in
Mathematics 227 (2011) 2327–2348 www.elsevier.com/locate/aim On a common …

Let $ M $ be a $(2\times n) $ non-generic matrix of linear forms in a polynomial ring. For
large classes of such matrices, we compute the cohomological dimension (cd) and the …

The F-threshold c J (a) of an ideal a with respect to an ideal J is a positive characteristic
invariant obtained by comparing the powers of a with the Frobenius powers of J. We study a …