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 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 …

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 …

Let R be a commutative noetherian ring. Denote by mod\, R mod R the category of finitely
generated R-modules. In this paper, we study n-torsionfree modules in the sense of …

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 …

We prove two theorems on the vanishing of Ext over commutative Noetherian local rings.
Our first theorem shows that, over non-regular Cohen-Macaulay local domains, there are no …

For a local ring $(R,\M) $ of infinite residue field and positive depth, we address the question
raised by H. Dao on how to control the asymptotic behaviour of the $\M $-full, full, and …

In the present paper, we study the Dao numbers $\mathfrak {d} _1 (I),\mathfrak {d} _2 (I) $
and $\mathfrak {d} _3 (I) $ of an ideal $ I $ of a Noetherian local ring $(R,\mathfrak {m}, K) …

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 …

Let R be a commutative Noetherian ring. Denote by mod R the category of finitely generated
R-modules. In this paper, we study dominant resolving subcategories of mod R. We …