Let R be a commutative noetherian ring. Lindo and Pande have recently posed the question
asking when every ideal of R is isomorphic to some trace ideal of R. This paper studies this …

An ideal I in a Noetherian ring R is normally torsion-free if Ass (R/It)= Ass (R/I) for all t≥ 1.
We develop a technique to inductively study normally torsion-free square-free monomial …

We describe coefficient ideals for both $(x, y) $-primary monomial ideals in $ k [x, y] $ and
$\mathfrak {m} $-primary ideals in two-dimensio-nal regular local rings $(R,\mathfrak {m}) …

Abstract Let\(I\subset S\) be a graded ideal of a standard graded polynomial ring S with
coefficients in a field K, and let\({\text {v}}(I)\) be the\({\text {v}}\)-number of I. In previous work …

Let $ I $ be a monomial squarefree ideal of a polynomial ring $ S $ over a field $ K $ such
that the sum of every three different ideals of its minimal prime ideals is the maximal ideal of …

Recently in [M. Jöllenbeck, On the multigraded Hilbert and Poincaré series of monomial
rings, J. Pure Appl. Algebra 207 (2)(2006) 261–298] the second author made a conjecture …

In this paper we define a two-sided ring of quotients of a ring R with 1, with respect to~ r
and~ z, arbitrary right and left Gabriel (idempotent) filters for R respectively. The two-sided …

In the 1950s, J.-P. Serre proved that the Poincaré series of a commutative local Noetherian
ring is component-wise bounded by a certain rational function depending on the Betti …

We characterize which complete local (Noetherian) rings T containing the rationals are the
completion of a countable excellent local ring S. We also discuss the possibilities for the …

We study when $ R\to S $ has the property that prime ideals of $ R $ extend to prime ideals
or the unit ideal of $ S $, and the situation where this property continues to hold after …