Let (R, m, k) be a normal Noetherian analytically irreducible universally catenary local
domain of dimension d≥ 1 with infinite residue field k and field of fractions K, and let I be an …

Let $(R,\mathfrak {m}) $ be an $ n $-dimensional regular local ring, essentially of finite type
over a field of characteristic zero. Given an $\mathfrak {m} $-primary ideal $\mathfrak {a} $ of …

The core of an ideal is the intersection of all its reductions. In 2005, Polini and Ulrich
explicitly described the core as a colon ideal of a power of a single reduction and a power of …

Using vanishing of graded components of local cohomology modules of the Rees algebra of
the normal filtration of an ideal, we give bounds on the normal reduction number. This helps …

In this paper, we study some algebraic invariants of t-spread ideals, t≥ 1, such as the
projective dimension and the Castelnuovo–Mumford regularity, by means of well-known …

In this paper we define and explore properties of mixed multiplicities of (not necessarily
Noetherian) filtrations of $ m_R $-primary ideals in a Noetherian local ring $ R …

For a regular ideal having a principal reduction in a Noetherian ring we consider the
structural numbers that arise from taking the Ratliff–Rush closure of the ideal and its powers …

Full article: An Upper Bound for the Regularity of Ideals of Borel Type Skip to Main Content
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It was previously known, by work of Smith–Swanson and of Sharp–Nossem, that the linear
growth property of primary decompositions of Frobenius powers of ideals in rings of prime …

Let I be a complete m-primary ideal of a regular local ring (R, m) of dimension d≥ 2. In the
case of dimension two, the beautiful theory developed by Zariski implies that I factors …