The notion of almost Gorenstein local ring introduced by V. Barucci and R. Fröberg for one-
dimensional Noetherian local rings which are analytically unramified has been generalized …

We introduce a new notion of commutative noetherian local rings, which we call dominant.
We explore fundamental properties of dominant local rings and compare them with other …

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 …

Consider a non-trivial fiber product $ R= S\times _kT $ of local rings $ S $, $ T $ with
common residue field $ k $. Given two finitely generated $ R $-modules $ M $ and $ N $, we …

Starting from the notion of totally reflexive modules, we survey the theory of Gorenstein
homological dimensions for modules over commutative rings. The account includes the …

We establish new results on (co) homology vanishing and Ext-Tor dualities, and derive a
number of freeness criteria for finite modules over Cohen-Macaulay local rings. In the main …

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 …

We study homological properties of test modules that are, in principle, modules that detect
finite homological dimensions. The main outcome of our results is a generalization of a …

There is given a characterization for the Rees algebras of parameters in a Gorenstein local
ring to be almost Gorenstein graded rings. A characterization is also given for the Rees …

The almost Gorenstein Rees algebras over two-dimensional regular local rings - ScienceDirect
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