The structure of the complex $\mathrm {\textbf {R} Hom} _R (R/I, R) $ is explored for an
Ulrich ideal $ I $ in a Cohen–Macaulay local ring $ R $. As a consequence, it is proved that …

The notion of 2-almost Gorenstein local ring (2-AGL ring for short) is a generalization of the
notion of almost Gorenstein local ring from the point of view of Sally modules of canonical …

Abstract The Auslander-Reiten conjecture is a notorious open problem about the vanishing
of Ext modules. In a Cohen-Macaulay complete local ring R with a parameter ideal Q, the …

The Cohen–Macaulay type of idealizations of maximal Cohen–Macaulay modules over
Cohen–Macaulay local rings is closely explored. There are two extremal cases, one of …

Ulrich ideals in numerical semigroup rings of small multiplicity are studied. If the semigroups
are three-generated but not symmetric, the semigroup rings are Golod, since the Betti …

We further develop the theory of generalized Ulrich modules introduced in 2014 by Goto et
al. Our main goal is to address the problem as to when the operations of taking the Hom …

We study the class of one-dimensional Cohen–Macaulay local rings with canonical
reductions, ie, admit canonical ideals which are reductions of the maximal ideals, show that …

The structure of Ulrich ideals in hypersurfaces - ScienceDirect Skip to main contentSkip to article
Elsevier logo Journals & Books Search RegisterSign in View PDF Download full issue Search …

We prove new results concerning the connection between (relative) reduction numbers and
the Castelnuovo-Mumford regularity of blowup algebras and blowup modules. A key basic …

The notion of commutative rings is important in singularity theory, and it is deeply related to
various algebraic areas, say, algebraic geometry, representation theory, invariant theory …