Historically, commutative algebra, whose foundations were laid by Dedekind, Hilbert,
Noether, and Krull, has developed in step with algebraic geometry, number theory …

We introduce the notion of Burch ideals and Burch rings. They are easy to define, and can
be viewed as generalization of many well-known concepts, for example integrally closed …

On reflexive and 𝐼-Ulrich modules over curve singularities Main Article Contents Mathematics
References Article Info Settings On reflexive and -Ulrich modules over curve singularities By …

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In this note we study trace ideals of canonical modules. Characterizations of the trace ideals
in terms of annihilators of certain Ext modules are given. We apply our results to study many …

For a numerical semigroup ring K [H] we study the trace of its canonical ideal. The colength
of this ideal is called the residue of H. This invariant measures how far is H from being …

Over an arbitrary commutative ring, correspondences among three sets, the set of trace
ideals, the set of stable ideals, and the set of birational extensions of the base ring, are …

Levelness and nearly Gorensteinness are well-studied properties of graded rings as a
generalized notion of Gorensteinness. In this paper, we compare the strength of these …

Tight closure test ideals have been central to the classification of singularities in rings of
characteristic $ p> 0$, and via reduction to characteristic $ p> 0$, in equal characteristic 0 as …

We introduce the notion of Burch submodules and weakly m-full submodules of modules
over a local ring (R, m) and study their properties. One of our main results shows that Burch …