Determinantal rings and varieties have been a central topic of commutative algebra and
algebraic geometry for several decades. Numerous researchers have contributed to the …

This note has two goals. The first is to give a short and self contained introduction to the
Castelnuovo–Mumford regularity for standard graded rings R=⊕ i∈ ℕ R i over general base …

We give a simple proof for the fact that the Castelnuovo–Mumford regularity and related
invariants of products of powers of ideals are asymptotically linear in the exponents …

We investigate the asymptotic behavior of Castelnuovo-Mumford regularity of Ext and Tor,
with respect to the homological degree, over complete intersection rings. We derive from a …

We study the question of finite generation of saturated multi-Rees algebras and investigate
the asymptotic behaviour of related length functions. In the setup of excellent local domains …

Abstract Set A:= Q/(z), where Q is a polynomial ring over a field, and z= z 1,…, zc is a
homogeneous Q-regular sequence. Let M and N be finitely generated graded A-modules …

Let $ X $ be an $ m\times n $ matrix of distinct indeterminates over a field $ K $, where $
m\le n $. Set the polynomial ring $ K [X]:= K [X_ {ij}: 1\le i\le m, 1\le j\le n] $. Let $1\le k< l\le n …