Related papers: Injective modules and fp-injective modules over va…

Let $p$ be a prime number, $K$ be the henselization of the rational functions over the finite field $\mathbb{F}_p$ and $R$ be the ring of additive polynomials over K. We show that the field of Laurent series over $\mathbb{F}_p$ is decidable…

Let R be a local complete ring. For an R-module M the canonical ring map R\to End_R(M) is in general neither injective nor surjective; we show that it is bijective for every local cohomology module M := H^h_I(R) if H^l_I(R) = 0 for every…

We introduce the notion of admissible injective envelope for a locally C*-algebra and show that each object in the category whose objects are unital Fr\'{e}chet locally C*-algebras and whose morphisms are unital admissible local completely…

In this paper, we address various aspects of divisibility by irreducibles in rings consisting of integer-valued polynomials. An integral domain is called atomic if every nonzero nonunit factors into irreducibles. Atomic domains that do not…

We introduce the notion of strong $p$-semi-regularity and show that if $p$ is a regular type which is not locally modular then any $p$-semi-regular type is strongly $p$-semi-regular. Moreover, for any such $p$-semi-regular type, "domination…

In this paper, we construct indecomposable integrally closed modules of arbitrary rank over a two-dimensional regular local ring. The modules are quite explicitly constructed from a given complete monomial ideal. We also give structural and…

We provide algebraic conditions ensuring the decidability of the theory of modules over effectively given Pr\"ufer (in particular B\'ezout) domains whose localizations at maximal ideals have dense value groups. For B\'ezout domains, these…

In this paper, the notion of strongly G_C-projective and injective modules is introduced, where C is a semidualizing module. Using these modules we can obtain a new characterization of G_C-projective and injective modules, similar to the…

Let $\mathcal{S}$ be a class of finitely presented $R$-modules such that $R\in \mathcal{S}$ and $\mathcal{S}$ has a subset $\mathcal{S}^*,$ with the property that for any $U\in \mathcal{S}$ there is a $U^*\in \mathcal{S}^*$ with $U^*\cong…

We study the conditions under which the highest nonvanishing local cohomology module of a domain $R$ with support in an ideal $I$ is faithful over $R$, i.e., which guarantee that $H^c_I(R)$ is faithful, where $c$ is the cohomological…

Let $R=k[x,y]$ be a polynomial ring over a field $k$ of prime characteristic $p$ and let $E$ denote the injective hull of $k$ (which is isomorphic to $H^2_{(x,y)}(R)$). We prove that $E$ is not an injective object in the category of graded…

We prove that a group $G$ is locally finite if and only if every surjective real (or complex) linear cellular automaton with finite-dimensional alphabet over $G$ is injective.

By the Telescope Conjecture for Module Categories, we mean the following claim: "Let R be any ring and (A, B) be a hereditary cotorsion pair in Mod-R with A and B closed under direct limits. Then (A, B) is of finite type." We prove a…

Generalizing F-nilpotent completion for a ring spectrum F we first define the notion of completion with respect to a thick subcategory in a monogenic stable homotopy category. Specializing this to the thick subcategory generated by…

Let $G$ be a finite group and $H$ a normal subgroup of prime index $p$. Let $V$ be an irreducible ${\mathbb F}H$-module and $U$ a quotient of the induced ${\mathbb F}G$-module $V\kern-3pt\uparrow$. We describe the structure of $U$, which is…

In this paper we consider the locally self-injective property of the product FI$^m$ of the category FI of finite sets and injections. Explicitly, we prove that the external tensor product commutes with the coinduction functor, and hence…

Let $M$ be a left module over a ring $R$ and $I$ an ideal of $R$. We call $(P, f)$ a (locally)projective $I$-cover of $M$ if $f$ is an epimorphism from $P$ to $M$, $P$ is (locally)projective, $Kerf\subseteq IP$, and whenever $P=Kerf+X$,…

Let $\Lambda$ be a $\mathbb{Z}$-graded artin algebra. Two classical results of Gordon and Green state that if $\Lambda$ has only finitely many indecomposable gradable modules, up to isomorphism, then $\Lambda$ has finite representation…

We construct examples of noetherian three-dimensional local geometrically normal domains of prime characteristic which are $F$-injective but not $F$-full. Along the way, we find examples of two-dimensional local geometrically normal domains…

Let $R$ be a commutative noetherian ring and $I$ an ideal of $R$. Assume that for all integers $i$ the local cohomology module $H_I^i(R)$ is $I$-cofinite. Suppose that $R_\mathfrak{p}$ is a regular local ring for all prime ideals…