Related papers: On the projectivity of finitely generated flat mod…
In this paper, we study the relation between $m$-strongly Gorenstein projective (resp. injective) modules and $n$-strongly Gorenstein projective (resp. injective) modules whenever $m \neq n$, and the homological behavior of $n$-strongly…
We study totally acyclic complexes of projective modules over triangular matrix rings and then use it to classify Gorenstein projective modules over such rings. We also use this classification to obtain some information concerning…
In this paper we study projective flat deformations of projective spaces. We prove that the singular fibers of projective flat deformations of projective spaces appear either in codimension 1 or over singular points of the base. We also…
Let k be an algebraically closed field of characteristic zero. Let f:X-->S be a flat, projective morphism of k-schemes of finite type with integral geometric fibers. We prove existence of a projective relative moduli space for semistable…
We give some functorial characterizations of flat strict Mittag-Leffler modules. We characterize reflexive functors of modules with similar tools, definitions and theorems.
We explore some properties of wide subcategories of the category mod$\,(\Lambda)$ of finitely generated left $\Lambda$-modules, for some artin algebra $\Lambda.$ In particular we look at wide finitely generated subcategories and give a…
We develop in this paper a stable theory for projective complexes, by which we mean to consider a chain complex of finitely generated projective modules as an object of the factor category of the homotopy category modulo split complexes. As…
We discuss the projectivity of the moduli space of semistable vector bundles on a curve of genus $g\geq 2$. This is a classical result from the 1960s, obtained using geometric invariant theory. We outline a modern approach that combines the…
The aim of this paper is to investigate properties of endo-prime and endo-coprime modules which are generalizations of prime and simple rings, respectively. Various properties of endo-coprime modules are obtained. Duality-like connections…
Let $R$ be a commutative ring. An $R$-module $M$ is said to be $w$-split if Ext$_{R}^1(M,N)$ is a GV-torsion $R$-module for all $R$-modules $N$. It is known that every projective module is $w$-split, but the converse is not true in general.…
We study finitely generated projective modules over noncommutative tori. We prove that for every module $E$ with constant curvature connection the corresponding element $[E]$ of the K-group is a generalized quadratic exponent and,…
Quasi-projective dimension of modules over associative rings is generalized in this paper to the one of complexes of modules. Basic properties of this dimension are established, including a comparison result with projective dimension and a…
In a previous article (J. Algebra 367 (2012), 142-165) we established axiomatic parametrised Cohen-Macaulay approximation which in particular was applied to pairs consisting of a finite type flat family of Cohen-Macaulay rings and modules.…
This book is an introductory course to basic commutative algebra with a particular emphasis on finitely generated projective modules. We adopt the constructive point of view, with which all existence theorems have an explicit algorithmic…
As a special case of Bass' theory of perfect rings, one obtains the assertion that, over a finite-dimensional associative algebra over a field, all flat modules are projective. In this paper we prove the following relative version of this…
Gorenstein homological dimensions are refinements of the classical homological dimensions, and finiteness singles out modules with amenable properties reflecting those of modules over Gorenstein rings. As opposed to their classical…
Very flat and contradjusted modules naturally arise in algebraic geometry in the study of contraherent cosheaves over schemes. Here, we investigate the structure and approximation properties of these modules over commutative noetherian…
This book is an introductory course to basic commutative algebra with a particular emphasis on finitely generated projective modules, which constitutes the algebraic version of the vector bundles in differential geometry. We adopt the…
We study the interconnection between the finite projective modules for a fuzzy sphere, determined in a previous paper, and the matrix model approach, making clear the physical meaning of noncommutative topological configurations.
In the work we have considered Breuil-Kisin module over the ring of witt vectors $W(\kappa)$ over the residue field $\kappa$ of characteristic $p$ and a finite flat $\mathbb{Z}_p$-algebra $R$. Then considered Breuil-Kisin modules $M$ over…