Related papers: Pure-injective hulls of modules over valuation rin…

In this paper we study injective modules over universal enveloping algebras of finite-dimensional Lie algebras over fields of arbitrary characteristic. Most of our results are dealing with fields of prime characteristic but we also…

We classify indecomposable pure injective modules over domestic string algebras, verifying Ringel's conjecture on the structure of such modules.

Let $\text{Red}(M)$ be the sum of all reduced submodules of a module $M$. For modules over commutative rings, $\text{Soc}(M)\subseteq \text{Red}(M)$. By drawing motivation from how $\text{Soc}$-injective modules were defined by Amin et. al.…

Warfield proved that every injective module has the exchange property. This was generalized by Fuchs who showed that quasi-injective modules satisfy the exchange property. We extend this further and prove that a module invariant under…

For an acyclic quiver $Q$ and a finite-dimensional algebra $A$, we give a unified form of the indecomposable injective objects in the monomorphism category ${\rm Mon}(Q,A)$ and prove that ${\rm Mon}(Q, A)$ has enough injective objects. As…

The cohomology annihilator of a noetherian ring that is finitely generated as a module over its center is introduced. Results are established linking the existence of non-trivial cohomology annihilators and the existence of strong…

A complex $X$ is called Ding injective if there exists an exact sequence of injective complexes $\ldots \rightarrow E_1 \rightarrow E_0 \rightarrow E_{-1} \rightarrow \ldots$ such that $X = Ker(E_0 \rightarrow E_{-1})$, and the sequence…

In this paper, the notions of nonnil-injective modules and nonnil-FP-injective modules are introduced and studied. Especially, we show that a $\phi$-ring $R$ is an integral domain if and only if any nonnil-injective (resp.,…

Let $S$ be a semiring. An $S$-semimodule $M$ is called a multiplication semimodule if for each subsemimodule $N$ of $M$ there exists an ideal $I$ of $S$ such that $N=IM$. In this paper we investigate some properties of multiplication…

For a commutative ring $S$ and self-orthogonal subcategory $\mathsf{C}$ of $\mathsf{Mod}(S)$, we consider matrix factorizations whose modules belong to $\mathsf{C}$. Let $f\in S$ be a regular element. If $f$ is $M$-regular for every $M\in…

Yet another proof of the result asserting that a morphism of commutative rings is an effective descent morphism for modules if and only if it is pure is given. Moreover, it is shown that this result cannot be derived from Moerdijk's descent…

We prove that for a noetherian semilocal ring $R$ with exactly $k$ isomorphism classes of simple right modules the monoid $V^*(R)$ of isomorphism classes of countably generated projective right (left) modules, viewed as a submonoid of…

Countably generated projective modules that are relatively big with respect to a trace ideal were introduced by P. P\v{r}\'ihoda, as an extension of Bass' uniformly big projectives. It has already been proved that there are a number of…

Let R be a commutative Noetherian ring of prime characteristic and M be an x-divisible right R[x,f]-module that is Noetherian as R-module. We give an affirmative answer to the question of Sharp and Yoshino in the case where R is semi-local…

Let $R$ be a commutative ring and $S \subseteq R$ be a multiplicative subset. We introduce and study the concept of $S$-purity based on the notion of $S$-strongly flat modules. The class of $S$-pure injective modules will be studied. We…

In a recent article, Iyama and Marczinzik showed that a lattice is distributive if and only if the incidence algebra is Auslander regular, giving a new connection between homological algebra and lattice theory. In this article we study when…

Let $M$ be a non-zero finitely generated module over a finite dimensional commutative Noetherian local ring $(R,\mathfrak{m})$ with dim$_R(M)=t$. Let $I$ be an ideal of $R$ with grade$(I,M)=c$. In this article we will investigate several…

The primary goal of this paper is to investigate the structure of irreducible monomorphisms to and irreducible epimorphisms from finitely generated free modules over a noetherian local ring. Then we show that over such a ring,…

In this note, we work out a simple inductive proof showing that every polyhedral cone K is the conic hull of a finite set X of vectors. The base cases of the induction are linear subspaces and linear halfspaces of linear subspaces. The…

Let R be a commutative noetherian ring. Let M be a finitely generated R-module. In this paper, we reconstruct M from its Koszul homology with respect to a suitable sequence of elements of R by taking direct summands, syzygies and…