Related papers: Bass modules and embeddings into free modules

Fisher [Fis75] and Baur [Bau75] showed independently in the seventies that if $T$ is a complete first-order theory extending the theory of modules, then the class of models of $T$ with pure embeddings is stable. In [Maz4, 2.12], it is asked…

A classical theorem of Hechler asserts that the structure $\left(\omega^\omega,\le^*\right)$ is universal in the sense that for any $\sigma$-directed poset P with no maximal element, there is a ccc forcing extension in which…

We show that an abelian category can be exactly, fully faithfully embedded into a module category as the right perpendicular subcategory to a set of modules or module morphisms if and only if it is a locally presentable abelian category…

In this paper, we introduce and study the concept of CS-Rickart modules, that is a module analogue of the concept of ACS rings. A ring $R$ is called a right weakly semihereditary ring if every its finitly generated right ideal is of the…

We give new proofs of two results of Stafford, which generalize two famous Theorems of Serre and Bass regarding projective modules. Our techniques are inspired by the theory of basic elements. Using these methods we further generalize…

Categorical constructions on heaps and modules over trusses are considered and contrasted with the corresponding constructions on groups and rings. These include explicit description of free heaps and free Abelian heaps, coproducts or…

We investigate homological and depth-theoretic properties of finitely generated modules of finite projective dimension over Noetherian local rings. A central theme is the study of criteria for freeness and reflexivity derived from the…

We introduce a lattice structure as a generalization of meet-continuous lattices and quantales. We develop a point-free approach to these new lattices and apply these results to $R$-modules. In particular, we give the module counterpart of…

Let $(R, \mathfrak{m}, k)$ be a commutative Noetherian local ring. We study the suitable chains of semidualizing $R$-modules. We prove that when $R$ is Artinian, the existence of a suitable chain of semidualizing modules of length…

In the representation theory of finite-dimensional algebras, the study of projective presentations of maximal rank is closely related to the study of generically $\tau$-regular irreducible components of varieties of modules over such…

In this paper we prove that if R is a left Noetherian and left regular ring such that all finitely generated projective left R-modules are stably free, then the same is true for the completion R[[x;\sigma,\delta]] of any Ore extension…

Let $R$ be a commutative noetherian ring admitting a dualizing complex and let $\mathfrak p$ be a prime ideal of $R$. In this paper we investigate when $G(R/\frak p)$ is an $R_{\frak p}$-module. We give some necessary and sufficient…

Let $(R,\m)$ and $(S,\n)$ be commutative Noetherian local rings, and let $\phi:R\to S$ be a flat local homomorphism such that $\m S = \n$ and the induced map on residue fields $R/\m \to S/\n$ is an isomorphism. Given a finitely generated…

We construct examples of bounded below, noncontractible, acyclic complexes of finitely generated projective modules over some rings $S$, as well as bounded above, noncontractible, acyclic complexes of injective modules. The rings $S$ are…

We study some closely interrelated notions of Homological Algebra: (1) We define a topology on modules over a not-necessarily commutative ring $R$ that coincides with the $R$-topology defined by Matlis when $R$ is commutative. (2) We…

We classify (up to quasi-isomorphism) the free differential modules whose homology is equal to a given module $M$ by developing a theory for deforming an arbitrary free complex into a differential module. We use an iterative approach to…

We prove that for every uncountable cardinal $\kappa$ such that $\kappa^{<\kappa}=\kappa$, the quasi-order of embeddability on the $\kappa$-space of $\kappa$-sized graphs Borel reduces to the embeddability on the $\kappa$-space of…

Let $\Gamma^\infty$ be the set of all universally Baire sets of reals. Inspired by recent work of the second author and Nam Trang, we introduce a new technique for establishing generic absoluteness results for models containing…

Let R be a ring (not necessarily commutative). A left R-module is said to be cotorsion if Ext 1 R (G, M) = 0 for any flat R-module G. It is well known that each pure-injective left R-module is cotorsion, but the converse does not hold: for…

A definition of quasi-flat left module is proposed and it is shown that any left module which is either quasi-projective or flat is quasi-flat. A characterization of local commutative rings for which each ideal is quasi-flat (resp.…