Related papers: When $\delta$-semiperfect rings are semiperfect

The goal of this paper is twofold. First, we write down the semi-infinite Pl\"ucker relations, describing the Drinfeld-Pl\"ucker embedding of the (formal version of) semi-infinite flag varieties in type A. Second, we study the homogeneous…

In our previous paper [GSV2020], we proved that the complementary components of a ring domain in $\mathbb{R}^n$ with large enough modulus may be separated by an annular ring domain and applied this result to boundary correspondence problems…

In the Lubin-Tate setting we compare different categories of $(\varphi_L,\Gamma_L)$-modules over various perfect or imperfect coefficient rings. Moreover, we study their associated Herr-complexes. Finally, we show that a Lubin Tate…

Let $T$ be a local (Noetherian) ring and let $Q_1$ and $Q_2$ be prime ideals of $T$. We find sufficient conditions for there to exist a quasi-excellent local subring $B$ of $T$ satisfying the following conditions: (1) the completion of $B$…

Let $G$ be a group. A ring $R$ is called a graded ring (or $G$-graded ring) if there exist additive subgroups $R_{\alpha }$ of $R$ indexed by the elements $\alpha \in G$ such that $R=\bigoplus_{\alpha \in G}R_{\alpha }$ and $R_{\alpha…

We develop a general theory of partial morphisms in additive exact categories which extends the model theoretic notion introduced by Ziegler in the particular case of pure-exact sequences in the category of modules over a ring. We relate…

In this paper we define and study quasipolar general rings (with or without identity) and extend many of the basic results to the wider class. We obtain some new characterizations of quasipolar and strongly $\pi$-regular elements by using…

The objective of this paper is to introduce and study completions and local homology of comodules over Hopf algebroids, extending previous work of Greenlees and May in the discrete case. In particular, we relate module-theoretic to…

Starting from the notion of totally reflexive modules, we survey the theory of Gorenstein homological dimensions for modules over commutative rings. The account includes the theory's connections with relative homological algebra and with…

In representation theory of finite-dimensional algebras, (semi)bricks are a generalization of (semi)simple modules, and they have long been studied. The aim of this paper is to study semibricks from the point of view of $\tau$-tilting…

We introduce rational semimodules over semirings whose addition is idempotent, like the max-plus semiring, in order to extend the geometric approach of linear control to discrete event systems. We say that a subsemimodule of the free…

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.…

Inspired by a question raised by Eisenbud-Musta\c{t}\u{a}-Stillman regarding the injectivity of maps from ${\rm Ext}$ modules to local cohomology modules and the work by the third author with Pham, we introduce a class of rings which we…

We consider ring extensions whose set of all subextensions is stable under the formation of sums, the so-called Delta extensions and exhibit new examples of these extensions.

In this paper, we give semiring version of some classical results in commutative algebra related to Euclidean rings, PIDs, UFDs, G-domains, and GCD and integrally closed domains.

This study provides a comprehensive investigation into the structure and properties of a novel class of rings known as $\Delta$-quasipolar rings, in which for every $a\in R$ there exisxt $p^2=p \in comm^2(a)$ such that $a+p \in \Delta(R)$.…

Let R be a commutative ring and C a semidualizing R-module. In this article, we introduce and investigate the notion of DC-projective complexes. We first prove that a complex X is DC-projective if and only if each degree of X is a…

Let $R$ be a commutative ring with $ 1 \neq 0$. We recall that a proper ideal $I$ of $R$ is called a semiprimary ideal of $R$ if whenever $a,b\in R$ and $ab \in I$, then $a\in \sqrt{I}$ or $b\in \sqrt{I}$. We say $I$ is a {\it weakly…

For a restricted Lie algebra $L$, the conditions under which its restricted enveloping algebra $u(L)$ is semiperfect are investigated. Moreover, it is proved that $u(L)$ is left (or right) perfect if and only if $L$ is finite-dimensional.

The aim of this work is to study duality of fractional ideals with respect to a fixed ideal and to investigate the relationship between value sets of pairs of dual ideals in admissible rings, a class of rings that contains the local rings…