Related papers: Commutative rings whose finitely generated ideals …

Inspired from the work of P. Scholze on the finiteness of \(\mathbf{F}_{p}\)-cohomology groups of proper rigid-analytic varieties over \(p\)-adic fields, Zavyalov recently introduced the notion of almost coherent rings, which plays a key…

It is well-known that a ring R is semiperfect if and only if R as a left (or as a right) R-module is a supplemented module. Considering weak supplements instead of supplements we show that weakly supplemented modules M are semilocal (i.e.,…

Let $T$ be a subset of a ring $A$, and let $M$ be an $A$-module. We study the additive subgroups $F$ of $M$ such that, for all $x \in M$, if $tx \in F$ for some $t \in T$, then $x \in F$. We call any such subset $F$ of $M$ a $T$-factroid of…

It is shown that a commutative B\'ezout ring $R$ with compact minimal prime spectrum is an elementary divisor ring if and only if so is $R/L$ for each minimal prime ideal $L$. This result is obtained by using the quotient space…

In earlier work, the author classified rigid representations of a quiver by finitely generated free modules over a principal ideal ring. Here we extend the results to representations of a quiver by finitely generated projective modules over…

We address two aspects of finitely generated modules of finite projective dimension over local rings and their connection in between: embeddability and grade of order ideals of minimal generators of syzygies. We provide a solution of the…

In this paper, we introduce a new homological invariant called quasi-projective dimension, which is a generalization of projective dimension. We discuss various properties of quasi-projective dimension. Among other things, we prove the…

The following representation theorem is proven: A partially ordered commutative ring $R$ is a subring of a ring of almost everywhere defined continuous real-valued functions on a compact Hausdorff space $X$ if and only if $R$ is archimedean…

This paper is a commutative algebra introduction to the homological theory of quasi-coherent sheaves and contraherent cosheaves over quasi-compact semi-separated schemes. Antilocality is an alternative way in which global properties are…

Very flat and contradjusted modules naturally arise in algebraic geometry in the study of contraherent cosheaves over schemes. Here, we investigate the structure and approximation properties of these modules over commutative noetherian…

Let $(R, \frak m)$ denote a local Cohen-Macaulay ring and $I$ a non-nilpotent ideal of $R$. The purpose of this article is to investigate Faltings' finiteness dimension $f_I(R)$ and equidimensionalness of certain homomorphic image of $R$.…

In this article, we introduce and study the concept of $\phi$-2-absorbing quasi primary ideals in commutative rings. Let $R$ be a commutative ring with a nonzero identity and $L(R)$ be the lattice of all ideals of $R$. Suppose that…

We make a detailed study of idempotent ideals that are traces of countably generated projective right modules. We associate to such ideals an ascending chain of finitely generated left ideals and, dually, a descending chain of cofinitely…

We provide a certain direct-sum decomposition of reflexive modules over (one-dimensional) Arf local rings. We also see the equivalence of three notions, say, integrally closed ideals, trace ideals, and reflexive modules of rank one (i.e.,…

Let $R$ be a commutative ring. A quasi-Gorenstein $R$-module is an $R$-module such that the grade of the module and the projective dimension of the module are equal and the canonical module of the module is isomorphic to the module itself.…

Let $k$ be a commutative ring, $H$ a faithfully flat Hopf algebra with bijective antipode, $A$ a $k$-flat right $H$-comodule algebra. We investigate when a relative Hopf module is projective over the subring of coinvariants $B=A^{{\rm…

We consider the class of all commutative reduced rings for which there exists a finite subset T of A such that all projections on quotients by prime ideals of A are surjective when restricted to T. A complete structure theorem is given for…

In this work, the set of quasi-primary ideals of a commutative ring with identity is equipped with a topology and is called quasi-primary spectrum. Some topological properties of this space are examined. Further, a sheaf of rings on the…

We apply the theory of cotorsion pairs to study closure properties of classes of modules with finite projective dimension with respect to direct limit operations and to filtrations. We also prove that if the ring is an order in an…

A minimum depth d^I(S --> R) is assigned to a ring homomorphism S --> R and a R-R-bimodule I. The recent notion of depth of a subring d(S,R)in a paper by Boltje-Danz-Kuelshammer is recovered when I = R and S --> R is the inclusion mapping.…