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 describe new classes of noetherian local rings R whose finitely generated modules M
have the property that Tor i R (M, M)= 0 for i≫ 0 implies that M has finite projective …

We analyze whether Ulrich modules, not necessarily maximal CM (Cohen-Macaulay), can
be used as test modules, which detect finite homological dimensions of modules. We prove …

Let XX be a resolving subcategory of an abelian category. In this paper we investigate the
singularity category D_ sg (X)= D^ b (mod\, X)/K^ b (proj (mod\, X)) D sg (X ̲)= D b (mod X …

We answer a question of Celikbas, Dao, and Takahashi by establishing the following
characterization of Gorenstein rings: a commutative noetherian local ring (R,\mathfrak m)(R …

We obtain various characterizations of commutative Noetherian local rings (R, m) in terms of
homological dimensions of certain finitely generated modules. Our argument has a series of …

Let S be a deeply embedded, equicharacteristic, Artinian Gorenstein local ring. We prove
that if R is a non-Gorenstein quotient of S of small colength, then every totally reflexive R …

Our purpose in this work is multifold. First, we provide general criteria for the finiteness of the
projective and injective dimensions of a finite module $ M $ over a (commutative) …

We study a modified version of the classical Ulrich modules, which we call $ c $-Ulrich.
Unlike the traditional setting, $ c $-Ulrich modules always exist. We prove that these …

Two left noetherian rings R and S are said to be singularly equivalent if their singularity
categories are equivalent as triangulated categories. The aim of this paper is to give a …