Related papers: max-projective modules

For a commutative noetherian ring $R$, we classify all the hereditary cotorsion pairs cogenerated by pure-injective modules of finite injective dimension. The classification is done in terms of integer-valued functions on the spectrum of…

Let $R$ be a ring. It is proved that $(\mathcal{GP}(R), \mathcal{GP}(R)^\bot)$ is a complete hereditary cotorsion pair, where $\mathcal{GP}(R)$ denotes the class of the Gorenstein projective left $R$-modules. Then we get that each left…

Let $R$ be an arbitrary ring and $(-)^+=\Hom_{\mathbb{Z}}(-, \mathbb{Q}/\mathbb{Z})$ where $\mathbb{Z}$ is the ring of integers and $\mathbb{Q}$ is the ring of rational numbers, and let $\mathcal{C}$ be a subcategory of left $R$-modules and…

Let R be a commutative ring with identity and S a multiplicative subset of R. The aim of this paper is to study the class of commutative rings in which every S-flat module is flat (resp., projective). An R-module M is said to be S-flat if…

A ring is called $n$-perfect ($n\geq 0$), if every flat module has projective dimension less or equal than $n$. In this paper, we show that the $n$-perfectness relate, via homological approach, some homological dimension of rings. We study…

In the past, it has been shown that the Leavitt path algebra $L(E)=L_K(E)$ of a graph $E$ over a field $K$ is left and right noetherian if and only if the graph $E$ is finite and no cycle of $E$ has an exit. If $Q(E)=Q_K(E)$ denotes the…

Motivated by the definition of nearly Gorenstein rings, we introduce the notion of full-trace modules over commutative Noetherian local rings--namely, finitely generated modules whose trace equals the maximal ideal. We investigate the…

A module is called coneat injective if it is injective with respect to all coneat exact sequences. The class of such modues is enveloping and falls properly between injectives and pure injectives. Generalizations of coneat injectivity, like…

Let A be a commutative Noetherian ring of dimension d and let P be a projective R=A[X_1,\ldots,X_l,Y_1,\ldots,Y_m,\frac {1}{f_1\ldots f_m}]-module of rank r\geq max {2,dim A+1, where f_i\in A[Y_i]. Then (i) \EL^1(R\op P) acts transitively…

Let $(R, \mathfrak{m})$ be a Noetherian local ring. In this paper, we introduce a dual notion for dualizing modules, namely codualizing modules. We study the basic properties of codualizing modules and use them to establish an equivalence…

We introduce and investigate ss-injectivity as a generalization of both soc-injectivity and small injectivity. A module M is said to be ss-N-injective (where N is a module) if every R-homomorphism from a semisimple small submodule of N into…

Let $(R, \mathfrak{m})$ be a commutative Noetherian local ring with total quotient ring $K$. An $R$-module $M$ is called simple divisible, if $M$ is divisible $\neq 0$, but every proper submodule $0 \neq U \subsetneqq M$ is not divisible.…

As an alternative perspective on the injectivity of a pure-injective module, a pure-injective module M is said to be pi-indigent if its subinjectivity domain is smallest possible, namely, consisting of exactly the absolutely pure modules. A…

This paper introduces the notion of uniformly-S-pseudo-injective (u-S-pseudo-injective) modules as a generalization of u-S-injective modules. Let R be a ring and S a multiplicative subset of R. An R-module E is said to be…

We prove the following;Theorem:Let R be a prime noetherian ring with k.dimR = n, n a finite non-negative integer. We refer the reader to the definitions (1.1) of this paper.For a fixed non-negative integer m, m<n let Xm be the full set of…

For four wide classes of topological rings $\mathfrak R$, we show that all flat left $\mathfrak R$-contramodules have projective covers if and only if all flat left $\mathfrak R$-contramodules are projective if and only if all left…

A left $R$-module $M$ is called two-degree Ding projective if there exists an exact sequence $...\longrightarrow D_{1}\longrightarrow D_{0}\longrightarrow D_{-1}\longrightarrow D_{-2}\longrightarrow...$ of Ding projective left $R$-modules…

We investigate finiteness conditions on modules of bounded projective dimension and their connection with generalized notions of coherence. For a ring $R$, we consider the class $\mathsf{FP}_n^{\le d}(R)$ of finitely $n$-presented modules…

Let $R$ be a commutative ring. An $R$-module $M$ is said to be super finitely presented if there is an exact sequence of $R$-modules $\cdots\rightarrow P_n\rightarrow\cdots \rightarrow P_1\rightarrow P_0\rightarrow M\rightarrow 0$ where…

We prove that if $R$ is a commutative Noetherian ring, then every countably generated flat $R$-module is quite flat, i.e., a direct summand of a transfinite extension of localizations of $R$ in countable multiplicative subsets. We also show…