Related papers: On some criteria for the balanced projectivity of …

Motivated by the Pontryagin-Hill criteria of freeness for abelian groups, we investigate conditions under which unions of ascending chains of projective modules are again projective. Several extensions of these criteria are proved for…

In this note, we establish conditions under which the union of an increasing sequence of completely decomposable modules over domains are again completely decomposable. In our investigation, the condition of purity of modules is crucial. In…

We generalize known results on summands of completely decomposable and separable torsion-free abelian groups to modules over h-local Pr\"ufer domains. Over such domains summands of completely decomposable torsion-free modules are again…

We prove that moduli spaces of torsion-free sheaves on a projective smooth complex surface are irreducible, reduced and of the expected dimension, provided the expected dimension is large enough. Actually we prove more: given a line bundle…

In this work, we investigate conditions under which unions of ascending chains of modules which are isomorphic to direct sums of ideals of an integral domain are again isomorphic to direct sums of ideals. We obtain generalizations of the…

A procedure resolving a torsion-free coherent sheaf on a nonsingular $N$-dimensional projective algebraic variety into a locally free sheaf on a projective scheme of certain class is proposed. This is a higher-dimensional analog of the…

In this paper, we study the problem when a finitely generated torsionless module is projective. Let $\Lambda$ be an Artinian local algebra with radical square zero. Then a finitely generated torsionless $\Lambda$-module $M$ is projective if…

We characterize projective objects in the category of internal crossed modules within any semi-abelian category. When this category forms a variety of algebras, the internal crossed modules again constitute a semi-abelian variety, ensuring…

In this article, the projectivity of finitely generated flat modules of a commutative ring are studied from a topological point of view. Then various interesting results are obtained. For instance, it is shown that if a ring has either a…

I classify projective modules over idempotent semirings that are free on a monoid. The analysis extends to the case of the semiring of convex, piecewise-affine functions on a polyhedron, for which projective modules correspond to convex…

Drinfeld recently suggested to replace projective modules by the flat Mittag--Leffler ones in the definition of an infinite dimensional vector bundle on a scheme $X$. Two questions arise: (1) What is the structure of the class $\mathcal D$…

Let $A$ be a ring of dimension $d$ containing an infinite field $k$, $T_1,\ldots,T_r$ be variables over $A$ and $P$ be a projective $A[T_1,\ldots,T_r]$-module of rank $n$. Assume one of the following conditions hold. (1) $2n\geq d+3$ and…

We study (relative) K-Mittag-Leffler modules, with emphasis on the class K of absolutely pure modules. A final goal is to describe the K-Mittag-Leffler abelian groups as those that are, modulo their torsion part, aleph_1-free, Cor.6.12.…

We construct monads for framed torsion-free sheaves on blow-ups of the complex projective plane at finitely many distinct points. Using these monads we prove that the moduli space of such sheaves is a smooth algebraic variety. Moreover we…

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 prove that every non-finitely generated projective module over the integral group ring of a polycyclic-by-finite group G is free if and only if G is polycyclic.

We construct projective moduli spaces for torsion-free sheaves on noncommutative projective planes. These moduli spaces vary smoothly in the parameters describing the noncommutative plane and have good properties analogous to those of…

Let $X$ be a smooth, irreducible, projective algebraic surface, and let $\alpha \in \mathbb{Q}[m]_{>0}$ be a polynomial. In this paper, we determine topological and geometric properties of the moduli space of $\alpha$-stable coherent…

Constructive proofs of fact that a stably free left $S$-module $M$ with rank$(M)\geq$sr$(S)$ is free, where sr$(S)$ denotes the stable rank of an arbitrary ring $S$, were developed in some articles. Additionally, in such papers, are…

For a finite dimensional Frobenius cellular algebra, a sufficient and necessary condition for a simple cell module to be projective is given. A special case that dual bases of the cellular basis satisfying a certain condition is also…