Related papers: Almost Cohen-Macaulay and almost regular algebras …

This work concerns finite free complexes over commutative noetherian rings, in particular over group algebras of elementary abelian groups. The main contribution is the construction of complexes such that the total rank of their underlying…

Faltings; Gabber and Ramero introduced almost mathematics. In another way, almost mathematics can be characterized bilocalization abelian category of modules mentioned in Quillen's unpublished note. Applying the concept of Quillen's…

Let $A$ and $B$ be commutative Noetherian algebras over an arbitrary field $\Bbbk$ such that $A \otimes_\Bbbk B$ is Noetherian. We consider ideals $I$ and $J$ of $A$ and $B$, respectively, as well as nonzero finitely generated modules $L$…

This is the first in a series of papers, where we introduce and study topological spaces that realize the algebras of quasi-invariants of finite reflection groups. Our result can be viewed as a generalization of a well-known theorem of A.…

In this paper, we study a relationship between tilting modules with finite projective dimension and dominant dimension with respect to injective modules as a generalization of results of Crawley-Boevey-Sauter, Nguyen-Reiten-Todorov-Zhu and…

In this paper, we introduce a new homological invariant called quasi-projective dimension, which is a generalization of projective dimension. We discuss various properties of quasi-projective dimension. Among other things, we prove the…

We studies the nearly Gorenstein property for Veronese subalgebras of (semi-)standard graded algebras. We introduce a condition~$(\natural)$ for Cohen--Macaulay semi-standard graded rings, motivated by the study of Ehrhart rings. We show…

Let $k$ be an infinite field of characteristic $p > 0$ and let $R = k[Y_1,\ldots, Y_d]$ (or $R = k[[Y_1,\ldots, Y_d]]$). Let $F \colon \text{Mod}(R) \rightarrow \text{Mod}(R)$ be the Frobenius functor and let $\mathcal{M}$ be a $F_R$-finite…

Let $A$ and $B$ be commutative rings with unity, $f:A\to B$ a ring homomorphism and $J$ an ideal of $B$. Then the subring $A\bowtie^fJ:=\{(a,f(a)+j)|a\in A$ and $j\in J\}$ of $A\times B$ is called the amalgamation of $A$ with $B$ along $J$…

We study Cohen-Macaulay non-Gorenstein local rings $(R,\mathfrak{m},k)$ admitting certain totally reflexive modules. More precisely, we give a description of the Poincar\'{e} series of $k$ by using the Poincar\'{e} series of a non-zero…

We investigate the geometry of almost Robinson manifolds, Lorentzian analogues of almost Hermitian manifolds, defined by Nurowski and Trautman as Lorentzian manifolds of even dimension equipped with a totally null complex distribution of…

We investigate homological properties of perfect algebras of prime characteristic. The principle is as follows: perfect algebras resolve the singularities. For example, we show any module over the ring of absolute integral closure has…

Let A be a Noetherian ring. It is shown that any finite A--module M of finite Krull dimension with finite Cousin complex cohomologies has a uniform local cohomological annihilator. The converse is also true for a finite module M satisfying…

We study moduli spaces of mirror non-compact Calabi-Yau threefolds enhanced with choices of differential forms. The differential forms are elements of the middle dimensional cohomology whose variation is described by a variation of mixed…

Let $(R,\fm)$ be a commutative Noetherian local ring. Suppose that $M$ and $N$ are finitely generated modules over $R$ such that $M$ has finite projective dimension and such that $\Tor^R_i(M,N)=0$ for all $i>0$. The main result of this note…

This paper investigates when local cohomology modules have an annihilator that does not depend on the choice of an ideal. Takahashi classified the dominant resolving subcategories of the category of finitely generated modules over a…

We study the topology of a class of proper submodules and some of its distinguished subclasses and call them structure spaces. We give several criteria for the quasi-compactness of these structure spaces. We study $T_0$ and $T_1$ separation…

Motivated by a recent result of Yoshino, and the work of Bergh on reducible complexity, we introduce reducing versions of invariants of finitely generated modules over commutative Noetherian local rings. Our main result considers modules…

Let $R$ be a commutative ring. A quasi-Gorenstein $R$-module is an $R$-module such that the grade of the module and the projective dimension of the module are equal and the canonical module of the module is isomorphic to the module itself.…

We prove that if M is a finitely-generated module of dimension d with finite local cohomologies over a Noetherian local ring, and if the ith local cohomology module of M is zero unless i = d, i = 0, and i = r for some r strictly between 0…