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 …

In this paper we study homological dimensions of finitely generated modules over
commutative Noetherian local rings, called reducing homological dimensions. We obtain …

The purpose of this paper is, as part of the stratification of Cohen–Macaulay rings, to
investigate the question of when the fiber products are almost Gorenstein rings. We show …

We consider a local (or standard graded) ring $ R $ with ideals $\mathcal {I}'$, $\mathcal {I}
$, $\mathcal {J}'$, and $\mathcal {J} $ satisfying certain Tor-vanishing constraints. We …

This paper deals with the subject of singularities of a germ of an analytic space given by the
gluing of germs of complex analytic spaces and some invariants such as degree of a finite …

In this paper, we show that the gluing of germs of formal complex spaces is also a formal
complex space. Moreover, we study the Betti numbers of the gluing of formal complex …

A local Cohen--Macaulay ring is called Ulrich-split if any short exact sequence of Ulrich
modules split. In this paper we initiate the study of Ulrich split rings. We prove several …

A semidualizing module is a generalization of Grothendieck's dualizing module. For a local
Cohen-Macaulay ring $ R $, the ring itself and its canonical module are always realized as …

In this paper we study the behavior of the Betti numbers of a finitely generated R-module
over the fiber product ring R× TS, with R, S and T being local rings with common residual …

Bounds for Multiplicities of the Graded Fiber Product Ring | Bulletin of the Brazilian Mathematical
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